Preheat the oven to 450°F (232°C).
In a medium skillet, cook the breakfast sausage over medium-high heat until browned and crumbled. Drain excess fat and set aside to cool slightly.
In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt.
Fold in the shredded cheddar cheese and the cooked sausage crumbles into the dry mixture.
Pour in the cold buttermilk and stir with a spatula until a wet, shaggy dough forms, ensuring no dry pockets remain.
Pour the melted butter into an 8x8-inch metal or glass baking pan, coating the bottom entirely.
Transfer the dough into the pan on top of the butter. Use a spatula to spread the dough evenly to the edges of the pan until it is submerged in the butter.
Use a knife or bench scraper to score the dough into a 3x3 grid to create 9 individual squares.
Bake for 20 to 25 minutes until the tops are deep golden brown and the butter has been fully absorbed by the biscuits.
Remove from the oven and allow to rest for 5 minutes in the pan before serving.