Place peppers on a baking sheet and roast for 20 minutes until the skins have become black and charred.
Once the peppers have cooled enough to handle, peal off and discard the skins, then dice the peppers.
Spread mayonnaise on the outside of each slice of bread.
Place a skillet over medium heat. Once heated, place 4 slices of bread (mayonnaise side down) on the skillet. Arrange cheese on top of the bread, add the diced poblano, then cover with the other side with bread (mayonnaise side up).
Flip sandwich in the skillet when the bottom side is golden brown to your liking. Cook until the other side is golden brown. Slice in half and enjoy!