Preheat the oven to 350 degrees F (175 degrees C). Grease 30 individual muffin cups or line cups with paper liners.
Beat 1 cup plus 2 tablespoons butter and white sugar in a large bowl with an electric blender until creamy. Add eggs one at a time and beat well after each addition. Beat in lemon zest and vanilla extract.
Combine flour, baking soda, baking powder, and salt in a separate bowl. Add to butter mixture alternately with sour cream and mix well into a thick batter. Spoon 1/4 cup of batter into each muffin cup.
Bake in the preheated oven until tops spring back when lightly pressed, 20 to 25 minutes. Cool in the tins for 10 minutes. Transfer to a wire rack and let cool, about 20 minutes.
Prepare the frosting while cupcakes are cooling. Cream together 1 cup plus 2 tablespoons butter and vanilla extract with an electric blender. Gradually beat in confectioners' sugar, 1 cup at a time, mixing well after each addition. Beat in milk and continue beating until frosting is light and fluffy.
Spread out marshmallow halves on a clean surface, cut-side down. Spread a little bit of frosting in the center of each marshmallow half. Sprinkle with pink decorating sugar to make the bunny ears.
Spread an even layer of frosting over each cooled cupcake. Place 2 of the prepared marshmallow halves on each cupcake for the ears. Place a chocolate piece in the middle of each cupcake for the nose and draw eyes and whiskers with black decorating gel.