Preheat oven to 375°F (190°C). Line a 12-cup muffin tin with liners or grease well.
In a large bowl, whisk together melted butter, sugar, eggs, and vanilla until smooth.
Stir in the sourdough discard and milk until well combined.
In a separate bowl, whisk together flour, baking powder, baking soda, and salt.
Gradually fold dry ingredients into the wet mixture until just combined (do not overmix).
If using mix-ins, gently fold them in.
Divide batter evenly into muffin cups, filling each about ¾ full.
Bake for 18–22 minutes, or until a toothpick inserted into the center comes out clean.
Cool for 5 minutes in the pan, then transfer to a wire rack.