Slice croissants: Preheat oven to 350°F. Line a large rimmed baking sheet pan with parchment paper; set aside. Slice croissants in half crosswise and lay both halves, cut sides up, on prepared baking sheet.
Assemble sandwiches: Spread ½ teaspoon of the Dijon mustard on each croissant half. Place 1 slice of ham and a half slice of both Swiss and Gruyère cheese on bottom halves of each croissant. Replace top halves; set aside.
Brush croissants with garlic butter: Microwave butter and garlic in a small microwave-safe bowl on HIGH until melted and sizzling, about 20 seconds. Brush tops of each croissant with butter mixture.
Bake croissants: Bake in preheated oven until cheese is melted and croissants are toasted and flaky, about 10 minutes. Serve immediately.
