In a bowl, whisk together eggs, whole milk, salt, and black pepper until well combined. Heat a nonstick skillet over medium-low heat and melt butter. Pour in the egg mixture and gently push the edges toward the center using a spatula. Cook until softly set and creamy.

While eggs are warm, split croissants in half. Spread a thin layer of Dijon mustard on each half. Layer ham, followed by scrambled eggs, and top with cheddar cheese. Place croissant top on the sandwich.

Preheat oven to 350°F. Arrange sandwiches on a baking sheet lined with parchment paper. Bake for 8-10 minutes until heated through and cheese melts.

For storage, wrap each sandwich tightly in aluminum foil. Store in resealable bags in the fridge for up to 3 days or freeze for up to 3 months. To reheat, remove foil and bake in a preheated oven at 325°F for 20-30 minutes.