Add the butter and sugar to a mixing bowl and whip until a creamy, gritty mixture forms.
Add the eggs and milk, then mix until fully incorporated.
Add flour, cinnamon, nutmeg, baking powder, and baking soda, then, mix on low speed, increasing speed as needed until no flour pockets remain.
Gently fold the shredded carrots by hand, using a wooden spoon or spatula, until evenly distributed throughout the batter.
Prepare the bundt pan by liberally greasing it. You can use cooking spray or shortening.
Pour the batter into the prepared bundt pan and smooth out the top. Drop the pan from 2” on a flat surface to shake out any bubbles.
Bake for 45-55 minutes or until the cake is done and a toothpick inserted into the middle comes clean.
Let cool for 10-15 minutes in the bundt pan before flipping onto a plate, cooling rack, or serving platter to cool completely.
To make the frosting, beat the cream cheese, vanilla and butter until creamy and combined well. Gradually add in the powdered sugar and whisk until combined and creamy.
Add the frosting to a piping bag to frost the bundt cake. Start in the center on top of a ridge or between a ridge, and pipe the frosting over the curve of your cake but not going all the way down the side.
Repeat this around the whole cake. You can also use a knife or frosting spatula to spread it around the bundt cake.
Top with chopped pecans, and enjoy!