Preheat oven to 425°F and line a sheet pan with parchment paper.

Cut zucchini into half-moons, halve cherry tomatoes, and trim asparagus. Toss vegetables with 2 tablespoons olive oil, salt, and black pepper.

Spread vegetables on prepared sheet pan and roast for 15-18 minutes until tender and lightly caramelized.

While vegetables roast, dice ham into 1/4-inch cubes. Dice bell peppers and onion into similar-sized pieces.

Heat 1 tablespoon butter in a large skillet over medium heat. Add onions and cook for 3-4 minutes until softened.

Add bell peppers and cook another 3 minutes. Add ham and cook 2 minutes more. Transfer mixture to a bowl.

Crack 8 eggs into a bowl, add 2 tablespoons milk, salt, and pepper. Whisk until well combined.

Heat remaining butter in the same skillet over medium-low heat. Pour in half the egg mixture.

As eggs begin to set, gently push cooked portions toward center, tilting pan to allow uncooked eggs to flow to edges.

When eggs are mostly set but still slightly wet on top, add half the ham-pepper mixture to one side.

Sprinkle with half the shredded cheese, then fold omelet in half. Cook 1 minute more until cheese melts.

Slide onto serving plate and repeat process with remaining ingredients for second omelet.

Cut each omelet in half and serve immediately with roasted vegetables on the side.

Garnish with fresh parsley if desired.