Preheat the oven to 350 degrees F (175 degrees C). Line 24 mini muffin tins with paper cups or grease with butter.
Combine flour, baking powder, cinnamon, and nutmeg in a bowl.
Beat sugar, milk, eggs, and vanilla extract together in a bowl using an electric mixer until creamy. Gradually add melted butter to the mixture. Add the flour mixture gradually, beating until combined. Fold in apples. Pour batter into the mini muffin cups.
Bake in the preheated oven until golden, about 15 minutes. Cool on a wire rack for 5 minutes. Run a table knife around the edges to loosen. Invert cupcakes carefully onto a serving plate or cooling rack. Let cool completely, at least 15 minutes, while making the icing.
Beat butter in a large bowl using an electric mixer until creamy. Gradually add sugar, milk, cinnamon, and nutmeg, beating until well blended. Spread icing over the cupcakes.
If using full-sized muffin cups, bake for about 40 minutes.
Substitute shortening for the butter if desired.
Nutrition data for this recipe includes the full amount of icing ingredients. The actual amount of icing consumed will vary.
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