Preheat oven t0 425 degrees and line a large baking sheet with parchment. You may need two baking sheets.
Heat 1 tbsp of olive oil in a cast iron skillet. Toss in mushrooms along with cumin, chili powder, oregano, salt and pepper. Let cook undisturbed for 4-5 minutes, then flip and turn and cook an additional 3-5 minutes until mushrooms begin to release their juices and soften. Pour in salsa verde, lower the heat, and simmer at least 10 minutes but up to 20. Remove from heat and let the sauce thicken slightly for about 5 minutes.
While the mushrooms simmer, blend all ingredients for honey jalapeno crema in a food processor or blender until smooth. Alternatively, you can finely chop all of the components and mix by hand, keeping in mind the finished product will be chunkier. Keep covered in the refrigerator until ready to serve.
Microwave tortillas for about 15 seconds under a layer of damp paper towels. Rub each, one both sides, with a dab of olive oil, from the reserved 2 tsp, and lay on the baking sheet. Sprinkle about 2 tbsp shredded cheese onto one half and top with a layer of salsa verde mushrooms. Gently fold the other half over the filling and press to adhere. Repeat with remaining tortillas and filling.
Bake for 8-10 minutes on one side, then flip and baking an additional 5-8 minutes. Remove from oven and let sit on the baking sheet for about 5 minutes - the tortillas will continue to crisp and be easier to handle.