Using a kitchen towel, gently rub off the charred skin from the pepper and discard. Remove the core and cut the flesh of the pepper into 1/8-inch strips.
Place 3 slices of bread on your work surface. Spread a thin layer of mayonnaise on one side of each slice. Arrange a quarter of the sliced avocado over the first slice of bread. Evenly space a few of the pepper strips over the avocado and sprinkle with salt and pepper. Place the second slice of bread, mayonnaise-side down over the avocado and peppers, then spread some more mayonnaise over the top.