In a medium bowl, whisk together the eggs, whole milk, salt, and black pepper until fully combined.
Heat a non-stick skillet over medium heat and melt the butter.
Pour the egg mixture into the skillet and cook, stirring gently, until the eggs are fully scrambled and cooked through, about 3-4 minutes. Remove from heat and set aside.
In a separate skillet, heat the vegetable oil over medium heat.
Add the breakfast sausage, breaking it up with a spatula, and cook until browned and cooked through, about 6-7 minutes. Remove sausage from skillet and drain on paper towels.
In the same skillet, add the thawed hash browns and cook until golden brown and crispy on both sides, about 5 minutes. Remove from heat.
To assemble each crunchwrap, lay one flour tortilla flat on a clean surface.
In the center of the tortilla, layer 1/4 of the scrambled eggs, 1/4 of the cooked sausage, 1/4 cup of crispy hash browns, 2 tablespoons of shredded cheddar cheese, 2 tablespoons of shredded Monterey Jack cheese, and 1 tablespoon of salsa.
Fold the edges of the tortilla up and over the filling, pleating as needed to form a sealed wrap.
Heat a large skillet or griddle over medium heat. Place the assembled crunchwrap seam-side down and cook for 2-3 minutes until golden brown and sealed.
Flip carefully and cook the other side for an additional 2-3 minutes until golden and the cheese is melted.
Repeat with the remaining tortillas and fillings.
Serve warm with optional sour cream on the side.