Step 1

Place the eggs in a large bowl and whisk until the whites and yolks are completely mixed and the eggs are a bit frothy. Whisk in the milk, salt, and pepper until just combined.

Step 2

Melt the butter in a large nonstick skillet over medium-low heat. Pour in the egg mixture and let sit undisturbed until the eggs just start to set around the edges, about 2 minutes. Using a rubber spatula, push the set eggs from the edges into the center. Spread the uncooked eggs back into an even layer. Repeat, pushing the set eggs from the edges into the center every 30 seconds until almost set, for a total cooking time of 6 to 8 minutes. (The top of the eggs should still be slightly wet.) Transfer the eggs to a bowl.

Step 3

To assemble the sandwiches, spread about 1 teaspoon of the mustard over the cut-side of each croissant bottom. Place a slice of ham over the bottom piece of each croissant. Top each with a heaping 1/2 cup of scrambled eggs and 1/4 cup of cheese. Place the top half of each croissant over the sandwich.

Step 4

To serve immediately: Arrange a rack in the middle of the oven and heat to 350°F. Place the sandwiches on a baking sheet. Bake until the cheese is melted, 8 to 10 minutes.Reheating: If not serving immediately, tightly wrap each sandwich with aluminum foil and store in resealable bags in the refrigerator or freezer. Reheat uncovered in a 325°F oven until warmed through, about 20 minutes if refrigerated, or about 30 minutes if frozen.