In a large mixing bowl, whisk together the brown sugar, eggs, coconut oil, and pumpkin purée until smooth. Stir in the sourdough starter.
Add the all-purpose flour, whole wheat flour, cinnamon, nutmeg, cloves, and water. Stir just until no dry streaks of flour remain. Cover the bowl with plastic wrap or a damp tea towel and leave in a warm place to ferment for 6–8 hours. If you're not ready to bake, refrigerate the batter for up to 24 hours.
Preheat the oven to 180°C (350°F). Sprinkle the baking soda, baking powder, and salt over the fermented batter, then gently stir just until incorporated. Do not overmix.
Divide the batter evenly between greased or paper-lined muffin cups, filling each one almost to the top.
Bake for 10–15 minutes, or until the muffins are well risen, golden brown, and a toothpick inserted into the center comes out clean. Cool in the pan for 5 minutes, then transfer to a wire rack to cool slightly before serving.