Prep. Preheat your oven to 400°F (200°C) and position the oven rack in the center. Then, line a 12-cup muffin tin with paper liners.
Mix the dry ingredients. In a large mixing bowl, whisk the flour, sugar, baking powder, and salt until well combined.
Add wet ingredients. Add the vegetable oil (or melted butter), milk, egg, and sourdough starter to the dry ingredients. Then, stir gently until just combined. Be careful not to overmix, as this can make the muffins dense.
Add the blackberries. With a spatula, carefully mix the blackberries into the batter without smashing them. This helps spread the berries evenly in the batter.
Assemble. Fill each muffin cup about ⅔ full with batter. Then, sprinkle the top of each muffin with a generous amount of coarse sparkling sugar.
Bake. Place the muffin tin in the preheated oven and bake for 18-23 minutes. Rotate the tin halfway through baking to make sure even cooking. The muffins are done when a toothpick inserted into the center comes out clean or with a few moist crumbs. The tops should be golden and slightly firm to the touch.
Cool and serve. Allow the muffins to cool in the tin for 5 minutes, then transfer them to a wire rack to cool completely. Serve warm or at room temperature.