Divide the 1 tablespoon butter between the two bread slices and spread the butter on one side of each slice.
Heat a grill pan or sauté pan over medium heat.
Place one bread slice butter-side down in the pan.
On the exposed (unbuttered) side of the bread in the pan, spread 1 1/2 teaspoons pesto.
Evenly sprinkle 1/4 cup shredded Gruyere and 1/4 cup shredded Monterey Jack over the pesto.
Arrange the 3 slices cooked chicken on top of the cheese and season the chicken with salt and freshly ground pepper to taste.
Add the 2 slices roasted red bell pepper if using.
Top with the second bread slice, butter-side up.
Cook over medium heat until the bottom slice is browned and the cheese is beginning to melt, then carefully flip the sandwich and continue cooking until the second side is browned and the cheese is completely melted, adjusting the heat as needed.
Remove from the pan, slice in half, and serve.