Char the poblanos on a grill or under the broiler until blackened all over. Place the charred poblanos in a bowl and cover until cool enough to handle. Wipe off the charred skins; seed and thinly slice.
In a large skillet, heat the oil over medium-high to high heat. Add the mushrooms and cook until darkened and softened, 7 to 8 minutes. Add the potatoes, onion, garlic, cumin, oregano, salt and pepper and cook for 10 minutes longer. Deglaze the pan with the beer and stir in the poblanos.
Spoon one-quarter of the filling onto 3 corn tortillas. Repeat for 3 more servings. Sprinkle the cheese on top. Squeeze the juice of the lime wedges over each portion and top with the cilantro and sour cream.
