Brush melted butter on one side of each slice of bread. Lay bread, buttered side down, on a large plate or cutting board. On two of the slices, spread pesto on the unbuttered side.
Next, layer cheese slices, chicken, and roasted red peppers onto other two slices of bread. Top with other slices of bread, buttered side out.
Heat a large non-stick skillet or griddle over medium heat. While the skillet heats, wrap the bottom of a large cast iron skillet in foil. (Note: If you have cast iron grill presses, you can skip wrapping a cast iron skillet and use those instead. You just need something weighted to help press and heat the sandwiches through.)
Add sandwiches to the heated skillet and gently lay the foiled cast iron skillet on top. Cook the sandwiches until golden brown on each side and heated through, about 3-4 minutes per side.
Slice sandwiches in half before serving and serve with tomato soup, if desired.