Place a rack in the upper third of your oven and preheat to 200°F This will keep the pancakes warmed as they’re fried in batches.
To make the pancakes: In a large bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg. In a small bowl, whisk together the egg, brown sugar, buttermilk and vanilla. Stir in carrots. Stir carrot mixture into dry ingredients, stirring until just Incorporated.
To make the cream cheese topping: In a small bowl, beat the cream cheese until fluffy and lump-free. Whisk in powdered sugar, two tablespoons milk, vanilla and cinnamon.
Over medium heat, melt 1 tablespoon butter in a cast-iron skillet or griddle pan. Spoon 2 tablespoons batter into the hot pan per pancake. flipping once, until pancakes are golden on both sides, about 2 minutes per side. Transfer finished pancakes to a serving dish or tray in the oven, to keep warm while you repeat the process with the remaining batter, adding more butter as needed.
Serve warm with cream cheese topping.