Luscious Carrot Cupcakes

Preheat oven to 350 degrees F (175 degrees C).

Mix 1/2 cup plus 2 tablespoons oil, eggs, brown sugar, and grated carrots together, in that order, in a bowl.

Mix flour, cinnamon, baking powder, vanilla sugar, and salt together in a separate bowl. Add flour mixture to oil mixture and stir to combine. Fill 12 cups of a muffin tin with the batter.

Bake on the middle rack of the preheated oven until a toothpick inserted in the center comes out clean, 12 to 15 minutes; do not overbake. Cool completely before frosting, about 45 minutes.

Mix confectioners' sugar, cream cheese, butter, lemon juice, and lemon zest together in a bowl; stir until the icing reaches a smooth, thick, and creamy texture. Cover icing with plastic wrap and refrigerate until set, at least 30 minutes, before topping cupcakes.