In a large cast-iron or other heavy skillet, heat 3 tablespoons oil over medium-high heat until smoking. Add the mushrooms and brown for 10 minutes. Add the remaining tablespoon oil, the bell pepper and onion, and cook, stirring, until crisp-tender, 2-3 minutes. Add the jalapeño, garlic and thyme; season with salt and pepper. Cook, tossing for 2-3 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 skillet.
Fill the hot tortillas with the Manchego, mushroom filling, tomato and cilantro. Tuck in the sides, wrap and roll tightly into a burrito.