Heat a skillet over medium heat and cook sausages until browned and fully cooked, about 6–8 minutes. Transfer to a plate lined with paper towels.
Whisk eggs, milk, salt, and pepper in a bowl. Melt butter in a skillet, add the egg mixture, and cook slowly over low heat, stirring gently until soft scrambled and creamy. Remove from heat.
For crescent rolls, unroll and separate into 8 triangles, press seams together, and cut into 12 rectangles. For puff pastry, roll out and cut into 12 rectangles. For pancakes, cook 12 thin pancakes about 4–5 inches wide.
Place a spoonful of scrambled eggs, a sprinkle of cheese, and one sausage on each piece of dough or pancake. Roll tightly, tucking edges to seal, and place seam-side down on a parchment-lined baking sheet.
Preheat oven to 375°F (190°C). Brush with egg wash if using pastry. Bake 15–18 minutes until golden brown and puffed.
Serve warm with maple syrup, ketchup, or hot sauce for dipping.