Preheat the oven to 375°F (190°C) and line a baking tray with parchment paper.

Carefully slice the large croissants in half horizontally, layer with shredded cheddar and mozzarella cheeses, and brush egg on cut sides of croissant tops. Bake for 6-8 minutes.

Whisk together eggs with salt and pepper. Melt butter in a non-stick pan, pour egg mixture and scramble until softly set.

In the same pan, cook mortadella slices until crispy, adding mozzarella on top in the last minute.

Assemble by layering scrambled eggs, crispy mortadella, arugula, and drizzle with basil pesto on croissant bottoms, then place tops back on.