Preheat your oven to 425°F and line a 12-cup muffin pan with paper liners so everything is ready to go once your batter is mixed. Starting at a higher temperature helps these muffins rise quickly and gives you that soft center with a nicely domed top.
In a medium bowl, whisk together the flour, baking powder, and baking soda until evenly combined, then set the bowl aside while you mix the wet ingredients.
In a large bowl, whisk together the melted butter, sourdough starter, egg, sour cream, sugar, and vanilla extract until the mixture looks smooth and fully combined. If you still see a few light streaks from the starter, that is completely normal and will work itself out as the batter comes together.
Add the dry ingredients into the bowl with the wet ingredients and stir gently just until everything is incorporated. The batter should be thick and scoopable, not thin or runny, and it is better to stop mixing early than to overwork it. Fold in the poppyseeds until they are evenly distributed throughout the batter.
Divide the batter evenly between the muffin cups, filling each one almost to the top so they bake up with a full, rounded shape. If you like a little texture on top, sprinkle a small amount of turbinado sugar over each muffin before baking.
Place the pan in the oven and bake for about 18 minutes, or until the tops are set and a toothpick inserted into the center comes out clean. The muffins should feel lightly springy when pressed.
Let the muffins cool in the pan for a few minutes, then transfer them to a wire rack to cool the rest of the way so the bottoms do not trap steam.
Once completely cooled, store the muffins in an airtight container at room temperature for up to three days, or freeze them individually and reheat when you want something quick and homemade.