Preheat oven to 375 F.

Brush the insides of the muffins with 1/4 cup of the butter.

Place onto a baking sheet and bake until lightly golden and starting to get crispy around the edges.

Add 2 tablespoons of the remaining butter to a large over-safe skillet over medium-high heat.

Add the ham and brown on both sides. Remove.

Add remaining butter to the skillet.

Crack eggs into 4 silicon ring molds.

Sprinkle with thyme, salt and pepper.

Reduce heat to low and cook for 2 minutes or until the whites are almost done.

Transfer the skillet to the oven and cook another 2 minutes until the whites are cooked. Remove.

Spread mayonnaise on the muffin halves.

Add the cheese, ham, eggs, a few splashes of hot sauce and the muffin tops.

If desired, place the sandwiches in the oven for 5 minutes to lightly melt the cheese.