Heat olive oil in a large non-stick skillet over medium-high heat. Add diced potatoes, salt, pepper, and paprika. Cook, stirring occasionally, for 15-20 minutes, or until potatoes are tender inside and crispy golden brown outside. Remove from skillet and set aside.

In the same skillet (no need to clean), add the breakfast sausage. Cook over medium heat, breaking it apart with a spatula, until browned and cooked through, about 5-7 minutes. Drain any excess grease and set the sausage aside with the potatoes.

In a medium bowl, whisk together eggs, milk, salt, and pepper until well combined and slightly frothy. Melt butter in the same skillet over medium-low heat. Pour in the egg mixture. As the eggs begin to set, gently push them from the edges to the center with a spatula. Cook until eggs are softly scrambled but still moist, about 3-5 minutes. Do not overcook.

While eggs are scrambling, warm the flour tortillas. You can do this by heating them in a dry skillet over medium heat for about 15-30 seconds per side until pliable, or microwave them wrapped in a damp paper towel for 20-30 seconds.

Lay a warm tortilla flat. Down the center of each tortilla, spoon a portion of the scrambled eggs, then add the cooked potatoes, breakfast sausage, and a generous sprinkle of shredded cheddar cheese. If using, add a sprinkle of sliced green onions.

Fold the sides of the tortilla over the filling, then fold up the bottom edge tightly and roll the burrito upwards to create a secure, compact wrap.

Serve immediately with your favorite optional toppings like salsa, hot sauce, sour cream, or sliced avocado.