Preheat oven 350°. In a large bowl, beat butter and sugar until light and fluffy, 5-7 minutes. Add eggs, one at a time, beating well after each addition.
Beat in applesauce and vanilla (mixture may appear curdled). Combine the flour, baking powder and salt; add to the creamed mixture alternately with liqueur, beating well after each addition.
Fill paper-lined muffin cups two-thirds full. Bake until a toothpick inserted in the center comes out clean, 18-22 minutes. Cool for 10 minutes before removing from pans to wire racks to cool completely.
For frosting, in a large bowl, beat butter and cream cheese until fluffy. Beat in liqueur. Add confectioners’ sugar; beat until smooth. Pipe over tops of cupcakes. Refrigerate leftovers.