Preheat the oven to 375 degrees Fahrenheit.
Stuff each jalapeno half with approximately 1 ounce of cream cheese. Place the stuffed jalapenos on a baking sheet and bake for 25-30 minutes. Remove from the oven.
Assemble the sandwiches: Place 1 slice of cheddar cheese on 2 bread slices and 1 slice of Monterey Jack cheese on the other 2 bread slices. Each sandwich will have both kinds of cheese. Slice the cooked stuffed jalapenos into bite-size pieces and divide them between the 2 slices of bread with cheddar. Add the 4 slices of bacon to the slices of bread with Monterey Jack. If desired, add chopped cilantro to one side. Combine the slices of bread to form 2 sandwiches.
Top each sandwich with several pats of butter. Place the sandwiches in a skillet over medium-low heat, butter side down. Top with more pats of butter. Grill each side until lightly browned and the cheese is melted and gooey.