Preheat the oven to 350 degrees. Place paper liners in a 12-cup muffin tin.
Whisk the eggs and milk in a small bowl or measuring cup.
In a medium bowl, whisk together the flour, baking powder, cinnamon, and salt.
Using a large bowl and an electric mixer on medium-high, beat the butter and brown sugar until fluffy (about 3 minutes).
Lower the mixer speed to medium-low and add half the egg mixture, then half the flour mixture, beating well after each addition. Add the remaining egg mixture and flour mixture. Beat on medium speed for one minute.
Use a wooden spoon or spatula to fold in the grated carrots and pecans.
Divide the batter evenly between the muffin cups. Bake until the tops are gold and a tester inserted in the center comes out clean - about 22-25 minutes.
Cool in pan on a wire rack for 5 minutes. Remove cupcakes from the tin and place on a wire rack to cool completely.
Using a wooden spoon or a spatula, stir the cream cheese, vanilla, and honey together until smooth. Pipe or spread the icing on top of the cupcakes.