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Preheat the oven to 375°F (190°C). Unroll the crescent roll dough onto a baking sheet, press seams together to form a single crust, and bake for 8–10 minutes until lightly golden.
In a medium bowl, whisk together the eggs, milk, salt, and black pepper until frothy.
Melt the butter in a nonstick skillet over medium heat, pour in the egg mixture, and scramble until fully cooked and fluffy.
If using bell pepper and red onion, sauté them with the cooked sausage crumbles in a separate pan for about 3–5 minutes until slightly softened.
Let the crust cool briefly, then spread the scrambled eggs evenly over the top. Sprinkle the sausage–vegetable mixture (if used) over the eggs, then top with shredded cheddar cheese.
Return the pizza to the oven for 3–5 minutes, or until the cheese has melted.
Slice into servings and serve hot.