Roast the poblano over an open flame or under the broiler until charred all over, turning as necessary, about 8 minutes. Place in a bowl and cover with plastic wrap to steam and loosen the skin, about 5 minutes. When cooled, peel off the blackened outer skin. Slice into thin strips, and then into 1-inch pieces.
Cook the mushrooms in a medium skillet over medium-high heat with the olive oil. When almost softened, about 3 minutes, season with salt and pepper. Reserve.
Lay out 4 slices of the bread on a work surface. Layer each with 1 slice of cheese, about 1 tablespoon of the chopped poblanos, 1 tablespoon of the mushrooms and another slice of cheese. Brush a thin layer of chipotle in adobo sauce on the underside of the remaining bread and close the sandwiches. Thinly and evenly spread the butter on both sides of the bread using about 1 1/2 tablespoons of the butter for each sandwich.
Place 2 sandwiches into a medium skillet over medium heat. Cover the skillet with a lid and cook until the bread is evenly golden brown, about 2 minutes. Flip, cover again and cook until the bread is golden brown and the cheese is visibly melted, about 2 minutes more. Repeat with the remaining sandwiches.