Make the beer bread according to package directions (you can also use a loaf pan instead of a baking sheet for more uniform slices). Allow to cool.
Slice into 1-inch slices.
Butter one side of each slice. Top the buttered side with slices of cheese, then place another slice of bread, butter side towards the cheese, on top.
Cut into 1-inch cubes.
Repeat for all slices.
Pour 3 inches of oil into a pot and clip a deep fry thermometer onto the side. Bring oil to 350 degrees, adjusting heat to maintain this temperature.
In a medium bowl, mix together the flour, salt, pepper, and remaining 3/4 cup beer until well combined.
One at a time, drop the sandwich cubes into the batter, allowing excess to slide off.
Drop into the oil, frying on all sides until golden brown, or for about 2 minutes.