In a small bowl, combine the mustard, capers, and roasted garlic. Use a fork to mash the capers and garlic into a rough paste.
Spread the mustard mixture over one slice of bread. Spread the mayo over the outside of both slices of bread.
Heat the butter in nonstick skillet over medium heat. Add more if needed.
Once the butter has melted, place the mustard-coated slice of bread in the skillet, buttered side down. Layer the cheddar, sun-dried tomatoes, Gruyère, and Parmesan on top. Season with black pepper.
Top with the second slice of bread and cook until the underside is golden brown, about 3-4 minutes.
Carefully flip the sandwich and add the remaining butter to the skillet. Gently press down on the sandwich to encourage even browning and help the cheese melt.
Cook until the second side is golden brown and the cheese is fully melted, another 3-4 minutes. Slice in half, if desired, and serve.