Position a rack in the center of the oven and preheat to 425 degrees F. Line every other cup in 2 muffin pans with muffin liners, for a total of 12 cups. (This will allow the tops to spread and the muffins to bake more evenly.)
Cook the butter in a small saucepan over medium heat until melted and starting to brown, 3 to 4 minutes. Immediately pour the butter into a medium heatproof bowl and set aside.
Sift the flour, brown sugar, granulated sugar, cinnamon, ginger, cloves, baking powder, baking soda and salt into a large bowl. Set aside.
Add the oil, pumpkin puree and 2 tablespoons water to the brown butter. Whisk until combined, about 20 seconds. Add the eggs and vanilla and whisk until smooth and lightened, about 30 seconds.
Stir the liquid ingredients into the dry ingredients with a rubber spatula just until combined. Divide the batter evenly among the 12 liners (about a heaping 1/4 cup for each). Sprinkle the tops with the walnuts and pepitas. Sprinkle again with the raw sugar.
Place both muffin pans on the center oven rack and turn the oven temperature down to 375 degrees F. Bake, rotating the pans about 3/4 of the way through baking, until a toothpick inserted into the muffins comes out with a just a few moist crumbs clinging to it, 24 to 26 minutes. Let cool in the pans on a wire rack for 10 minutes. Remove the muffins from the pan and let cool completely on the rack.