In a large bowl, whisk together the eggs and milk. Season to taste with salt and pepper, then fold in the cheese; set aside.
Heat olive oil in a large nonstick skillet over medium heat. Add the onion and broccoli and saute for 5 minutes, or until broccoli is crisp-tender; season to taste with salt and pepper.
Pour the eggs over the vegetables and stir gently until eggs are just set. Set pan aside to cool before assembling the wraps.
Spoon a quarter of the eggs onto each wrap, spreading to cover, leaving a 1-inch border. Fold in the sides, then tightly roll up wrap from the bottom.
Cut wraps in half, if desired, and store in meal prep containers up to 4 days. To serve, reheat to steaming.
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Notes
To freeze, wrap each tightly in plastic wrap, then store in a zip-top freezer bag for up to 3 months. To serve, discard plastic wrap and set wrap on a plate. Cover with a damp paper towel and microwave for 2-3 minutes, or until steaming.