Dip green tomato slices into beaten egg, letting excess drip off. Press into cornmeal to coat both sides; shake off excess. Place coated slices on a plate.
STEP 2
Heat oil in a skillet over medium heat. Add coated tomato slices and cook until golden brown, about 2 to 3 minutes per side. Transfer to a paper towel to drain.
STEP 3
Wipe skillet clean and place over medium heat. Spread butter onto one side of each bread slice. Place 2 slices of bread, butter-side down, into the skillet.
STEP 4
Layer 3 slices of fried green tomato, 3 slices of red tomato, 1 slice of pepper Jack cheese, and jalapeno slices on top of each bread slice in skillet. Top with remaining bread, butter-side up. Cook until golden, then flip sandwiches and cook until golden brown on the other side.