Preheat the oven to 400 degrees. Spray muffin tins, or use liners, and set aside. Melt the butter in a small saucepan over low heat.
2. In a large bowl, use an electric mixer or a whisk to beat the eggs and sugar, about 2 minutes. Add the milk, melted butter, and carrots and mix well. Sift the flour, baking powder, baking soda, cinnamon (if desired), and salt over the egg mixture and stir until smooth. Gently fold in the nuts (if desired).
3. Spoon about 1/4 cup batter into each muffin cup. Bake on the middle shelf for about 20 minutes, or until a toothpick inserted in the center comes out clean.