Heat 1 tablespoon of the oil in a large skillet over medium-high heat. Add the mushrooms, poblano, garlic, ½ teaspoon salt, and ¼ teaspoon pepper.
Cook, tossing occasionally, until the vegetables are tender and the liquid has nearly evaporated, 6 to 8 minutes. Stir in the corn.
Heat broiler. Brush the tortillas with the remaining tablespoon of oil and place on a baking sheet. Broil until crisp, 1 minute per side.
Top with the cheese and broil until melted, about 1 minute. Top with the vegetables, lettuce, and salsa.