Preheat oven to 350F and generously grease a bundt pan with butter. Flour it lightly.
Grate carrots in a food processor or with a box grater. Set aside.
In a large bowl, whisk together all of the dry ingredients. Set aside.
Place all of the wet ingredients except for the carrots and pineapple in the bowl of a stand mixer with the paddle attachment. Blend well until everything is well combined and creamy. Add the dry ingredients and blend to form the batter. Add the grated carrots and pineapple and blend until combined.
Pour the batter into the bundt pan and bake in the oven for 45 minutes or until a toothpick inserted in the middle comes out clean. Let it cool for 20 minutes in the pan and then carefully run a butter knife around the edges to ensure it is loose. Carefully flip it onto a cooling rack to cool completely.
Once the cake is completely cooled, make the frosting by adding the cream cheese, butter, and icing sugar to a food processor with the paddle attachment. Blend on medium speed until it is light and fluffy Slowly add a little milk (1 tablespoon at a time) and blend. If needed, add a little more milk to reach the desired consistency. Drizzle over the cake and top with chopped pecans. Serve!