Preheat the oven to 400°F (205°C). Cover a large baking sheet with parchment paper to prevent sticking and simplify cleanup.
Place the pork sausage, grated sharp cheddar, sourdough discard, all-purpose flour, and melted butter in a large mixing bowl or the bowl of a stand mixer. Add grated onion, minced garlic, or paprika when using.
Blend the ingredients by hand or mix on low speed until they are evenly incorporated and form a unified dough.
Examine the consistency of the mixture. When the dough appears dry or does not hold its shape, add the milk gradually, beginning with 1 tablespoon. Mix only until the dough becomes cohesive without turning sticky. Avoid excessive mixing, which may produce a firmer texture.
Portion the dough with a tablespoon or small cookie scoop. Shape each portion into an evenly sized ball using approximately 1 tablespoon of dough.
Arrange the sausage balls across the prepared baking sheet, leaving a small amount of space between each piece.
Bake for 15–20 minutes, or until the sausage balls are golden on the outside and the sausage is fully cooked.
Remove the baking sheet from the oven and allow the sausage balls to rest for several minutes before serving.