In a large bowl of an electric mixer, beat butter on medium speed until creamy. Add brown and granulated sugars and vanilla; beat until smooth, lighter in color and fluffy. Add dry ingredients; mix on low speed until well-blended.
On a lightly floured surface, roll out dough to 1/4-inch thickness. Using cookie cutters dipped in flour, cut out cookies; place on a large cookie sheet(s) lined with parchment paper. Chill 10 minutes before baking.
For the Frosting: In a small bowl, whisk 2 tablespoons cream into powdered sugar until sugar dissolves and thickens. Continue adding cream 1 teaspoon at a time to achieve desired spreading consistency.