Preheat the oven to 375°F and line a 12-cup muffin tin with paper liners. I like to take some coconut oil on my hands and rub it over the top surface of the tin to ensure that if the muffins grow over the edge, they will not stick.
In a large bowl, beat the butter and brown sugar with an electric mixer until creamed, 2-3 minutes. Add the ripe bananas and mix until smooth.
Beat in the eggs, lemon juice, and vanilla extract. Carefully stream in the milk while mixing.
Add the flours, spices, baking soda, baking powder, and salt to the same bowl. Gently stir together on top with a spatula, then add the shredded carrots and mix the wet and the dry ingredients until just combined. The batter will become fairly thick as it sits.
Use a large ice cream scoop (equal to about ¼ cup measuring cup) to fill the lined muffin tin. Distribute the batter evenly among 12 muffins. They should be filled to the top.
Baking Tip: To achieve smooth, round muffin tops, take a spoon and run it under cold water. Dry lightly, then run the back of the spoon over the top of a muffin. This will smooth any spikey bits on the muffin top that could burn. Repeat, rinsing the back of the spoon before each muffin.
Top the muffins with chopped nuts and sprinkle with coarse sugar if desired. This will result in a nice crunchy muffin top.
Bake for 22-24 minutes until a toothpick inserted in a middle muffin comes out clean. Allow to cool in the pan for 10 minutes before removing to a wire rack. Enjoy warm or allow to cool completely.