Mix together the ground beef, chili seasoning mix, 2 minced chipotle peppers with adobo sauce, and the beer in a bowl. Divide the mixture evenly into three patties.
Stir together the mayonnaise and 1 minced chipotle pepper with adobo sauce in a small bowl. Divide the mixture between the bread slices and spread evenly. Place a slice of pepperjack cheese on top of the mayonnaise mixture on each slice of bread.
Heat a large skillet over medium-high heat. Cook the patties in the skillet until no longer pink in the center, 5 to 7 minutes each side for well done. Remove each burger to a slice of bread, sandwiching them with the remaining slices.
Drain the skillet, reserving 2 tablespoons of the grease. Heat the reserved grease in the skillet over medium-high heat. Grill the sandwiches in the skillet until the bread is golden brown and the cheese is melted, 1 to 2 minutes per side.