Preheat oven to 350°F and spray an 8x8-inch baking dish with non-stick cooking spray.
Cook sausage in a skillet over medium heat until slightly browned. Break the sausage apart using a wooden spatula as you cook.
Add onion and potato, season, and cook until potato is golden brown and onion softens.
In a small mixing bowl, whisk eggs and milk. Add ½ cup of the cheddar cheese, season with salt and pepper to taste, and mix to combine.
Place the sausage-potato mixture in the baking dish and stir in diced broccoli.
Pour the egg mixture evenly over the sausage, potato, and broccoli. Sprinkle the remaining cheddar cheese on top.
Bake for 30 to 35 minutes until the eggs are set and the potato is fully cooked through. Remove from oven and let cool before slicing. Garnish with fresh chives and serve.