1. Add the flour, baking powder, cinnamon, baking soda, and salt to a medium or large bowl, and whisk until thoroughly combined. Set aside.
2. In a separate large bowl, combine the sugar, brown sugar, oil, and butter, and beat with an electric mixer until fluffy. Make sure there are no large clumps of brown sugar. Add the eggs, one at a time, and mix until the last egg is just combined. Mix in the vanilla extract and sour cream.
3. Fold about ⅓ of the dry ingredients into the wet ingredients with a wooden spoon or silicone spatula, then pour in about ¼ cup of the buttermilk and stir. Continue alternating the dry ingredients and buttermilk until everything is incorporated and all of the ingredients are just combined. Try not to overmix. The batter will be thick.
4. Fold in the grated carrots, then cover the bowl loosely with plastic wrap or a tea towel. Let it rest at room temperature for 30 minutes. While the batter is resting, preheat the oven to 425°F.
5. Line 2 (12-cup) muffin tins with 6 liners each, one in every other cup. Use a cookie scoop to fill each liner to the top, about ¼ cup of batter each. Sprinkle some sanding sugar on top of each muffin.
6. Bake the muffins, one pan at a time (if needed, or 2 side by side on the top rack), for 5-6 minutes. Then, without opening the oven, lower the temperature to 350°F, and bake for another 13-16 minutes or until the muffins are tall and a toothpick inserted in the middle muffins comes out clean. Repeat with the second pan as needed.
7. Let the muffins rest in the pan for 10-15 minutes, then transfer to a cooling rack and let them cool to room temperature.

Cream Cheese Filling Option:

1. Prepare the cream cheese filling while the batter is resting. Beat the cream cheese, sugar, vanilla extract, and flour until smooth. Add the egg and beat until just combined. Transfer the cream cheese filling into a small piping bag with a small round tip, or just cut off the end of the bag about ½ inch up from the bottom.
2. Fill the muffin pan with ¼ cup of batter. Pipe the cream cheese filling into the center of each muffin, about 1 inch deep. Sprinkle the sanding sugar around the cream cheese center.
3. Bake the muffins according to the directions above.