I think what you will end up with is a dummy drawer at the top (to allow for the cook top guts) with two functional drawers below. Yes, it is your kitchen and you should insist on what you want. I have drawers under my cook top and love love love them!
Good luck!

I have two drawers under my 36'' Wolf range top. We built the cabinet ourselves and used 150 lb rated side mount slides.

Face frame on a 3/4'' plywood carcass. 1/2'' plywood box drawers (sides & bottoms of drawers are 1/2'' material.)

The Wolf range top is a heavy beast so I wouldn't want to put it on a frameless cabinet. The rest of our base cabs are a hybrid frameless but I wanted the extra heft of a framed cabinet for the Wolf.

Two drawers under my Capital Culinarian 36" rangetop hooked to natural gas.

I have a Dacor gas cooktop with drawers under it. Even though that is not the cooktop you want, I thought I would post since that is the brand your cabinet maker carries. According to the specs, the Dacor cooktop only needs 1/4 inch (6mm) Min. to combustibles below chassis.The sides of my drawer box did need to be cut down a little to clear the bottom/ chassis of the cooktop. The drawers needed some further adjustments in the front to back length of the drawer box to clear the gas regulator or some such part that hung down below the cooktop. Our GC installed the cooktop and his carpenter did the adjustments to my Amish built and installed cabinets. He also fashioned an angled piece of wood to the drawer box so that the drawer would be attached properly to the glides and still be able to have the soft close feature.
You certainly could have at least 2 drawers and possibly 3 under your cooktop. Here is a shot of my modified drawer.

I've got 2 under my BS range top. It's a heavy piece. The drawers don't go back as far as other drawers so there is plenty of room in the back to run the connections.

not that you need more photos to show your guy that it can be done, but here you go

Some of you appear to be confused about the difference between rangetops & cooktops. They're not the same thing.

A range top sets atop a cabinet, relying on the cabinet to supports its substantial weight. The controls are typically on the front of the appliance.

A cook top is suspended from the countertop and surrounded entirely by countertop. The controls are on the top surface of the cooker.

This is a "rangetop":

This is a "cook top":

You can do drawers under a Wolf Rangetop.
To do it with a WOLF you must have to reduce the depth of the top drawer as if it were in a 21" deep cabinet
OR work out a chase in it, I always do the former as the other is too risky to work out.
AND you have to have your shut off in a cabinet next to it.

You may be running into issues with what is available in the cabinet brand?

Mine is like Breezy's. The cabinet is reduced in height by the height of the rangetop and came with a solid top that the rangetop sits on. A small hole was cut in the back for the gas connection. You cannot have the shallow top drawer like badger's with a range top unless you reduce the depth of the lower drawer and have 2 of them -- which wastes valuable pot and pan space for most of us.

If you want the deep drawers, you should be fine, except that your cabinet maker isn't thinking. Just tell him to reduce the overall height by the amount needed to set your rangetop at the proper height (check Dacors' installation instructions and specs. I have a different brand and it sits withthe side at counter level, so take the thickness of your counter into account, and the grates sit above the counter) A standard cabinet comes with an open top and would not support the weight. Hope this is the only out of his box thing that throws him. It is an easy recovery if this is your only issue.

I just remembered Rhome410's Wolf rangetop. I believe out where she lives hers is hooked to liquid propane also, but I could be mistaken. I'll link her kitchen from her blog below. You can ask questions in the comment section of this blog post or email her. She's gracious about answering questions.

Here is a link that might be useful: Rhome410's kitchen and Wolf rangetop

Another rangetop owner (LP) with three drawers. The cabinetmaker is either uninformed or does not want to make drawers.

If your cabinets are factory made -it could pose a problem as the sizes are preset and not as flexible as customs. But it seems to me the 36 inch wide should be easy to match up with drawers. We are using the 36 in. stove top by Wolf and I plan on putting drawers under the stove top. So I am glad you are posting this question. Ours will not be propane-maybe the propane is an issue? Sometimes these contractors listen more to a man if you know what I mean, get hubby to be the bad guy in discussing this issue.

thanks, everyone. My cabinets are a semi-custom line (woodharbor). I was able to get to a spec sheet and they definitely have a "professional" rangetop cabinet pre-made with drawers, so I just have to insist on it. I know I may have to bring the back of the top drawer in a bit to make room for the "innards" but that's ok. kdjess, I think you may be right about getting the hubby in. He already said he'd be willing :)

I have a cooktop with a scooped out top drawer for utensils and 2 drawers below that for pots. First time I've had this set up. These are the most used in my kitchen and so, so essential. The only other option I would consider is open-front pull outs. For me these are love, love, love.