Most of our roof is sloped at 45 degrees, but the bit over the front porch slopes at 30 or less. For a while, there was a section on our front porch where we thought there was some sort of insect infestation, but it turns out, it's just water.

So, we got out our ladder and investigated. It appears that with that shallow slope, the water gets capillaried up the drip edge and then under the roof and down onto the porch rafters and headers (or whatever you call the top sills). It doesn't happen anywhere else bc thankfully, the pitch is steeper and the velocity of the water where the pitch is steeper seems to overcome any capillary tendencies.

Before I go commando with the caulk, which I know I shouldn't do but it's still tempting, can anyone recommend a drip edge for slate that would remedy this?