In a large bowl, using a mixer set on medium-high, beat together softened unsalted butter and sugar until fluffy. Add eggs, one at a time, followed by vanilla extract and salt. Reduce mixer speed to low and gradually add all-purpose flour, beating until ingredients are combined. (Dough will be slightly sticky.) Divide dough into 4 equal portions and cover each in plastic wrap, patting into 1/2-inch-thick squares. Chill until firm, about 2 hours or overnight. Preheat oven to 400 degrees F. On a floured surface, roll out dough, a square at a time, to 1/3 inch thick. Cut out cookies using ornament- or tag-shaped cutters. Transfer cookies to a parchment-lined baking sheet and chill for 10 minutes. Bake until lightly golden, about 12 minutes. Cool completely on pan or wire rack before decorating.