Preheat oven to 450°F (232°C).
Melt the unsalted butter and pour it into an 8x8-inch or 9x9-inch baking dish, ensuring the bottom is completely covered.
In a large mixing bowl, whisk together the flour, baking powder, salt, and sugar.
Fold in the cooked sausage crumbles and shredded cheddar cheese until evenly distributed through the dry mix.
Pour in the cold buttermilk and stir with a spatula just until a wet, shaggy dough forms. Do not overmix.
Transfer the dough into the baking dish, spreading it gently to the edges so the butter rises up the sides.
Using a bench scraper or knife, score the dough into a 3x3 grid to create 9 biscuit squares.
Bake for 20 to 25 minutes until the biscuits are golden brown and the butter has been mostly absorbed.
Remove from oven and let rest for 5 minutes before cutting along the score lines and serving.