In a medium mixing bowl, sift together flour, baking powder, baking soda, salt, cinnamon, allspice, and nutmeg. Set aside.
In a large mixing bowl, whisk together eggs, oil, vanilla, brown sugar, and buttermilk (or heavy cream with lemon juice).
Pour dry ingredients into the wet ingredients and stir with a spatula until most of the flour is mixed in. Add grated carrots and fold in until just combined.
Line a 12-tin muffin pan with muffin or cupcake liners or spray the inside with nonstick baking spray. Spoon enough batter into each mold so they are 90% full.
Bake in the oven on a rack in the top third of your oven for 20 to 25 minutes, or until a cake tester comes out clean.
Making the Glaze
Place cream cheese in medium microwave safe bowl and microwave on high for 10-20 seconds or until cream cheese is somewhat warm and a little runny. Stir gently and add in powdered sugar, vanilla extract and 1 tablespoon of milk; stir again and add more milk if necessary until glaze reaches desired consistency; not too runny and not overly thick.
Dip each muffin top into cream cheese glaze then place back on wire rack.