Preheat grill.
In a large bowl, toss peppers, onion, and tomatoes with olive oil, salt, and black pepper.
Place pepper halves, onion rings, and tomatoes on the grill. For the tomatoes, use a grilling basket or a silicone grilling mat to avoid them falling through the grate.
Grilled for about 5 to 7 minutes, turning the vegetables halfway through, until cooked through and slightly charred.
Remove from grill and set aside to cool slightly.
Once cool enough to handle, slice the peppers into thin strips.
Place balsamic vinegar in a small saucepan over medium-high heat. Bring to a rolling simmer and continue to cook until reduced by at least half, about 5 to 7 minutes. Remove from heat and stir in pepper and brown sugar.
Assemble the sandwiches by placing two slices of Cache Valley® Sharp Cheddar Cheese on two slices of bread each. Top each with half of the vegetables. Top with one more slice of cheese each. Drizzle with balsamic reduction and top with the other slices of bread.
In a large skillet over medium heat, melt 2 Tbsp butter. Place both sandwiches carefully in the skillet and cook until the cheese is melted on both sides. The bread should be golden brown and toasted. It will take you about 2 to 3 minutes per side.
Remove from heat and serve immediately.