Place a medium sauté pan over medium-high heat and add 2 tablespoons vegetable oil. When oil shimmers, add mushrooms and a generous pinch of salt. Sauté until mushrooms release their liquid, liquid evaporates and mushrooms begin to brown, about 10 minutes.

Add onions. Sauté, adjusting heat as necessary, until onions are soft and entire mixture is golden brown but not burned, about 5 minutes. Remove from heat and allow to cool slightly.

Using a food processor or a knife, finely chop mushroom-onion mixture, then transfer to a large bowl. Add grated cheeses, cilantro, oregano and coriander. Season to taste with salt and pepper.

Place a large nonstick or well-seasoned skillet over medium heat, and add remaining 2 tablespoons vegetable oil. Fill a tortilla with a spoonful of mushroom-cheese mixture, fold, and cook in skillet until browned and cheese is melted, about 5 minutes per side.

Repeat until all tortillas are filled and cooked. Serve immediately.