Preheat the oven to 375 degrees F (190 degrees C). Grease a 12-cup muffin pan or line with paper cups.

To make the cupcakes: Stir white sugar, vegetable oil, and eggs together in a large mixing bowl until thoroughly combined.

Whisk flour, baking powder, baking soda, cinnamon, and salt in a separate bowl.

Stir flour mixture into egg mixture until thoroughly moistened. Mix in carrot, pineapple, and 1 teaspoon vanilla extract.

Pour batter into the prepared muffin cups, filling them 3/4 full.

Bake in the preheated oven until muffin tops spring back when lightly pressed, about 20 minutes. Set aside to cool completely.

To make the frosting: Cream butter and cream cheese in a bowl with an electric mixer until smooth.

Beat in confectioners’ sugar, vanilla extract, and milk to make a spreadable frosting; frost the cooled cupcakes.