Adjust the oven rack to the middle position and heat the oven to 200°F. Set a wire rack inside a rimmed baking sheet. Process the cheddar, Brie, and wine in a food processor for 20 to 30 seconds until a smooth paste forms. Add the shallot and pulse 3 to 5 times to combine, then transfer the cheese mixture to a bowl. In a separate small bowl, stir the butter and mustard together until uniform.

Brush the butter-mustard mixture evenly over one side of each bread slice. Flip four of the slices over and spread the cheese mixture across the second side. Top with the remaining four bread slices, buttered-side up, and press down gently to help the sandwich layers adhere.

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 the bread is deeply golden and crisp, about 6 to 9 minutes per side. Reducing the heat ensures the thick cheese filling melts completely without scorching the bread.

Transfer the finished sandwiches to the wire rack in the warm oven. Wipe out the skillet with paper towels and repeat the process with the remaining two sandwiches. Serve warm, while the filling is molten and the bread is hot.