Position a rack in the center of the oven and preheat it to 350°F (175°C). Lightly brush the bottom and sides of a 9-by-13-inch (23-by-33-cm) baking dish with about 1 teaspoon of the melted butter.

Keep the rolls connected and place them on a cutting board. Using a large serrated knife, slice horizontally through the entire slab to create one top layer and one bottom layer. Work slowly so the rolls stay attached.

Place the bottom half of the rolls cut-side up in the prepared baking dish. Brush the cut surface with about 1 tablespoon of the melted butter, reaching the edges without saturating the bread.

Arrange the cheddar evenly over the bottom rolls, followed by the mozzarella. Spread the cheese all the way to the outer edges so each sandwich receives a similar amount. If using shredded cheese, keep it in an even layer rather than forming thick mounds.

Set the top half of the rolls over the cheese with the cut-side facing down. Press very lightly so the slab sits evenly, but do not compress the soft bread.

Whisk the remaining melted butter with the Dijon mustard, garlic powder, dried parsley, and salt. The mixture may look slightly separated, so stir it again immediately before brushing.

Brush the garlic butter over the tops and exposed sides of the rolls. Use a light, even coating, allowing a small amount to run between the individual rolls without pooling heavily in the bottom of the dish.

Cover the baking dish loosely with foil: Bake for 15 minutes, until the rolls are warm and the cheese has begun to melt. The center sandwiches may take slightly longer to heat than those around the edges.

Remove the foil and continue baking for 8 to 10 minutes. The tops should be golden and lightly crisp, and the cheese should be fully melted. If the rolls are browning too quickly, loosely return the foil to the pan.

Let the sandwiches rest for 5 minutes so the melted cheese settles slightly. Cut along the roll seams with a thin knife or separate them gently with a spatula. Serve warm with tomato soup, if using.