Preheat the oven to 350°F (175°C).
Divide the Gruyère and cheddar evenly between 2 slices of brioche bread. Top with the remaining bread slices to form 2 sandwiches.
Melt 2 tablespoons butter in a large skillet over medium heat.
Add the sandwiches to the skillet and cook for about 1 minute 30 seconds, or until the bottom is golden brown.
Flip the sandwiches and cook the other side for 40 seconds, just until lightly golden.
Transfer the sandwiches to a sheet pan. Spread 1 teaspoon butter over the top of each sandwich.
Bake for 4 minutes, or until the cheese is fully melted.
Slice in half and serve warm.