Preheat and prep. Heat oven to 425°F (220°C). Line a 12-cup muffin tin with paper liners or grease well.
Mix dry ingredients. In a large bowl, whisk together flour, sugar, baking powder, baking soda, and salt.
Mix wet ingredients. In a separate bowl, whisk sourdough discard, milk, melted butter, eggs, sour cream, and vanilla until smooth.
Combine. Pour the wet ingredients into the dry. Fold gently with a spatula until just combined — the batter should look lumpy. Stop as soon as no dry flour remains; do not overmix.
Add mix-ins. Fold in blueberries, chocolate chips, or your chosen mix-in with 2–3 gentle strokes.
Fill the tin. Use an ice cream scoop or spoon to divide batter evenly among the 12 cups, filling each about ¾ full. Sprinkle with coarse sugar if using.
Bake at high heat first. Bake at 425°F for 5 minutes — this gives the muffins a quick rise and a tall, domed top.
Lower heat and finish. Without opening the oven, reduce temperature to 350°F (175°C) and bake 13–17 more minutes, until a toothpick inserted in the center comes out clean.
Cool. Let muffins cool in the tin 5 minutes, then transfer to a wire rack.