Old-Fashioned Cupcakes

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1 3/4 cups cake flour (not self-rising)

1 1/4 cups unbleached all-purpose flour

2 cups sugar

1 tablespoon baking powder

3/4 teaspoon salt

2 sticks unsalted butter, cut into cubes

4 large eggs

1 cup whole milk

1 teaspoon pure vanilla extract

Old Fashioned Frosting, recipe follows

Old-Fashioned Frosting:

2 sticks butter, room temperature

8 cups confectioners' sugar

1/2 cup milk

2 teaspoons vanilla extract or other flavoring