Lemon cupcakes with lemon cream cheese frosting

The yellow part of the lemon peel has a strong lemon flavor and is used to flavor the cupcake batter and frosting. Be sure to wash and dry lemons before grating the peel, and to grate only the colored part of the rind (the white pith under the rind is bitter). The cake flour used here adds an especially tender texture to these cupcakes. It can be found in the baking section of supermarkets.

Cupcakes
1 1/4 cups cake flour
1 teaspoon baking powder
1/8 teaspoon salt
1/2 cup (1 stick) unsalted butter, at room temperature
1 cup sugar
2 large eggs
1 tablespoon lemon juice
2 teaspoons grated lemon zest
1 teaspoon vanilla extract
1/2 cup whole milk

Frosting
1/2 cup (1 stick) unsalted butter, at room temperature
4 ounces cream cheese, at room temperature
2 teaspoons finely grated lemon peel
1 teaspoon vanilla extract
2 cups powdered sugar

Glazed lemon peel
(OPTIONAL)
1 large lemon, washed
1/3 cup water
1/4 cup sugar
1 tablespoon cider vinegar