Adjust the oven rack to the middle position and heat to 200°F. Set a wire rack inside a rimmed baking sheet to keep the first batch of sandwiches crisp while the rest cook.

Process the cheddar, brie, and wine in a food processor until a smooth paste forms, 20 to 30 seconds. Add the shallot and pulse to combine, 3 to 5 pulses.

Combine the butter and mustard in a small bowl until smooth.

Brush the butter-mustard mixture evenly over one side of each slice of bread. Flip four slices over and spread the cheese mixture evenly across the unbuttered sides, then top with the remaining bread, buttered-side up.

Heat a 12-inch nonstick skillet over medium heat for 2 minutes. Place two sandwiches in the skillet, reduce the heat to medium-low, and cook until both sides are crisp and golden brown, 6 to 9 minutes per side.

Transfer the cooked sandwiches to the wire rack in the oven to stay warm. Wipe out the skillet with paper towels and repeat the process with the remaining sandwiches.

Serve immediately while the crust is still crisp and the center is molten.