Prepare the Bread: Place the sourdough slices on a clean work surface. Spread a thin layer of softened butter over one side of each slice. These buttered sides will become the outside of the sandwiches. Turn the bread over so the unbuttered sides face upward.

Add the Dijon: Spread a very thin layer of Dijon mustard over two slices of bread. The Dijon should complement the cranberry sauce rather than overpower it.

Build the Sandwiches: Divide half of the white cheddar between the two slices coated with Dijon. Layer the sliced turkey evenly over the cheese. Season the turkey lightly with freshly ground black pepper. Spoon the cranberry sauce over the turkey, spreading it gently without taking it completely to the edges. Add the Brie and remaining white cheddar. Sprinkle with fresh thyme if using. Top with the remaining bread slices, keeping the buttered sides facing outward.

Heat the Skillet: Place a large skillet over medium-low heat. Allow it to warm for 1–2 minutes. Using moderate heat is important because the bread needs enough time to become crisp while the cheese melts completely.

Grill the Sandwiches: Place the sandwiches in the skillet. Cook for approximately 3–4 minutes on the first side, gently pressing once with a spatula. When the bottom is deeply golden, carefully flip each sandwich.

Melt the Cheese: Cook the second side for another 3–4 minutes. If the bread is golden before the cheese has completely melted, reduce the heat to low and cover the skillet for approximately 30–60 seconds. Remove the lid as soon as the cheese is melted so the bread remains crisp.

Rest and Slice: Transfer the sandwiches to a cutting board. Allow them to rest for 1–2 minutes. This prevents the hot cheese and cranberry sauce from spilling out immediately when sliced. Cut each sandwich in half and serve warm.