Heat your oven to 350°F. Spray a muffin pan with nonstick cooking spray.
Add flour, baking soda, cinnamon, nutmeg, and salt to a medium bowl; stir to combine. Set aside.
In a food processor, add the carrots. Pulse until broken down into large pieces. Add coconut sugar, vegetable oil, applesauce, chia seeds, milk, and vinegar. Pulse again until carrots are broken down to grated texture.
Pour the ingredients from the food processor into the flour mixture. Stir until just combined (be careful not to over mix). Divide batter evenly between muffin containers.
Bake for 20 to 22 minutes. Insert a tester in the middle of one of the cupcakes to make sure it comes out clean. When done, remove from oven and cool for 5 to 7 minutes before transferring to a rack to cool some more.
Make cream cheese drizzle by placing vegan cream cheese in a microwave-safe bowl with maple syrup. Microwave for 30 seconds. Stir the cream cheese and maple syrup together. Add the vanilla and peanut butter powder and stir until you get a spreadable consistency. Drizzle over the top of each muffin.
Store muffins in an airtight container in the fridge for up to a week. You can freeze these muffins for up to two months.