In a large cast-iron or other heavy skillet, heat 3 tbsp. oil over medium-high heat until smoking. Add the mushrooms and brown for 10 minutes. Add the remaining 1 tbsp. oil, the bell pepper and onion and cook, stirring, until crisp-tender, 2 to 3 minutes. Add the jalapeno, garlic and thyme; season with salt and pepper. Cook, tossing, for 2 to 3 minutes.
Pour in the sherry to deglaze the pan; lower the heat to a simmer. Meanwhile, char the tortillas on each side over an open flame or in a dry skiller.
Fill the hot tortillas with the manchego, mushroom filling, tomato and cilantro. Tuck in the sides, wrap and roll tightly into a burrito.