In a large bowl or the bowl of a stand mixer, beat the butter until light. Stir in the cornstarch and sugar. Gradually add the flour mixing until a soft dough forms. (Dad mixes his by hand and shared that sometimes you have to ditch the spoon and just get your hands in there to form the dough). Form dough in to a ball and wrap tightly with plastic wrap. Refrigerate for about 30 minutes to chill.
On a lightly floured surface, roll your dough 1/4-inch thick. Take care to ensure that your dough is rolled as evenly as possible, so that cookies cook evenly. Using a cookie cutter, cut shapes and place on to an un-greased baking sheet. You can re-roll your scraps and cut more, as well. Once your cookies are cut, top with quartered glace cherries, sprinkles or nuts. Place cookie sheet with cookies in to the freezer for 10-15 minutes. (You can also freeze the cut dough in freezer bags once solid on the cookie sheet for up to 2 weeks and bake later or as needed.)
Preheat oven to 275°F with rack in centre of oven. Bake for about 30 minutes for cookies that have been lightly chilled. If cooking from frozen, they may take up to 45 minutes. Cookies should be firm but shouldn't brown at all, even around the edges. They really just dry as they cook.
Cool on racks then transfer to cookie tin or freeze. These cookies keep well and get better with age.