To make the tomato confit, combine the olive oil, cherry or grape tomatoes, and garlic cloves in a small pot. Simmer over low heat for about 15 to 20 minutes, or until the tomatoes are softened and begin to burst. Stir occasionally to ensure even cooking.
While the tomatoes cook, prepare the garlic butter spread. In a mixing bowl, stir together the Duke’s mayonnaise, melted butter, grated garlic, garlic powder, and dried parsley until well blended. Set the mixture aside.
Shred the cheddar, Gruyère, and Gouda cheeses and mix them together in a bowl. Spread a layer of the garlic butter on the inside of each sourdough slice, then top with a generous portion of the shredded cheese blend. Close each sandwich, then spread more garlic butter on the outer sides of the bread.
Preheat your griddle to medium-low heat. Place the assembled sandwiches on the griddle and cook until each side is golden brown and the cheese has melted completely.
Once cooked, open each sandwich slightly and spoon in some of the tomato confit. Close the sandwiches, slice, and serve immediately.