In a nonstick skillet over medium heat, melt 1 teaspoon of butter. Add the finely chopped shallot and ¼ teaspoon of fresh thyme, cooking for about 3-4 minutes until the shallots are softened and translucent. Set aside in a small bowl.

Spread 1 tablespoon of apple butter onto two slices of thick-sliced white bread or Texas toast. Layer the sautéed shallots over the apple butter, then add thinly sliced apples followed by a generous sprinkle of the shredded Alpine-style cheese and Havarti cheese. Top with another slice of bread.

In a small bowl, whisk together 1 large egg and 1 tablespoon of milk until well combined. This egg wash will create a golden-brown exterior.

Heat a skillet to medium and melt the remaining 1 teaspoon of butter. Place the sandwiches egg-side down in the skillet and brush the top with the egg wash. Cook for about 5 minutes until the bottom is golden brown and cheese begins to melt.

Add the remaining butter to the skillet before carefully flipping the sandwiches over. Cook uncovered for an additional 3-5 minutes until the second side is nicely browned and cheese is fully melted.