Place 8 slices of sourdough on a clean work surface. In a small bowl, mix the softened butter with the garlic powder until smooth. Spread butter evenly on one side of each bread slice (this will be the outside that contacts the pan). On the unbuttered side of 4 slices, spread about 1/2 teaspoon of Dijon mustard on each (this gives a subtle tang).

Assemble cheeses

Divide the cheeses into 4 equal piles: for each sandwich use 1/2 cup shredded sharp cheddar, 2 oz thinly sliced Gouda (about 2 slices), and 1/4 cup shredded Monterey Jack. Layer the cheeses on the mustard-spread side of each of the 4 bread slices: start with a thin layer of Monterey Jack (helps melt), then sharp cheddar, then Gouda. If using tomato slices or caramelized onions, add 2 tomato slices or ~1/4 cup caramelized onions per sandwich between the cheeses to keep them from making the bread soggy.

Close sandwiches

Top each assembled slice with the remaining 4 bread slices, buttered side facing out. Press gently to compact the sandwich so cheese layers make good contact but are not squeezed out.

Cook & finish

Preheat pan

Place a heavy skillet or cast-iron pan over medium-low heat. Add 1 tablespoon olive oil and 1 tablespoon melted butter to the pan and swirl to coat. The combination of oil and butter raises the smoke point while giving flavor and crispness.

Grill the sandwiches

Place 2 sandwiches in the pan (do not overcrowd). Cook for 3–4 minutes on the first side, pressing down gently with a spatula every 30–45 seconds to encourage even contact and melting. When the bottom is deeply golden brown (check by lifting a corner), carefully flip the sandwiches and cook 2–4 minutes more until the second side is golden and the cheese is fully melted. Reduce heat to low if the bread browns too quickly before the cheese melts. Repeat with the remaining 2 sandwiches, adding a touch more butter to the pan if needed.

Rest and slice

Transfer sandwiches to a cutting board and let rest 1 minute—this helps the melted cheese settle slightly. Using a sharp knife, cut each sandwich diagonally or in half, wiping the blade between cuts if cheese strings accumulate.

Season and serve

Sprinkle a light crack of freshly ground black pepper over each sandwich to finish. Serve hot. Optional: serve with pickles, tomato soup, or a simple green salad.