After some digging, this recipe came up as the best roll-out sugar cookie (despite the name). Since I haven't made them, I'm going to trust others' reviews, which (as far as I've seen) have been entirely positive. It's from Cook's Illustrated, November 2003. The recipe itself is subscription-only, but there seems to be a free video version (sans quantities). Of course, now I can't find the free video, so I'm going to post the recipe as is (Bee, I know you are a capable baker and don't need someone to show you how to use your stand mixer to combine ingredients!), and I'll add a link to the video if I find it again.
UPDATE: Found it! It should be the main video on this page.
UPDATE #2: Cook's Illustrated explains the method behind their unorthodox mixing strategy:
Creaming is a common method used in baking. Butter and sugar are whipped until light and fluffy, eggs are added, and then dry ingredients are incorporated gradually. This method delivers good results when making most cookies, but we found that it did not work well for rolled butter cookies (see Glazed Butter Cookies in the November/December 2003 issue of Cook's), and we wondered why.
Our recipe has two striking features: it contains no leavener (we did not want the cookies to puff) and very little liquid, not even from an egg. Because the dough is somewhat dry, the flour did not incorporate well when added at the end of the mixing process. As a result, the dough was unevenly mixed, with streaks of butter, which became sticky when handled. This streaking also had negative effects on the final baked product, as the pockets of butter led to puffed, uneven cookies. Butter is about 18 percent water, and when its temperature reaches 212 degrees Fahrenheit it turns to steam and expands dramatically, producing bubbles.
When we reversed the order of mixing and added the butter to the flour, the dough was much more uniform. There were no streaks of butter in the dough, so it did not stick when rolled. In addition, because the dough did not contain pockets of butter, the cookies did not puff in the oven, and the baked cookies had flat tops, ready for decorating.
Glazed Butter Cookies
Makes 36-40 2 1/2-inch cookies
If you cannot find superfine sugar, you can obtain a close approximation by processing regular granulated sugar in a food processor for about 20 seconds. If desired, the cookies can be finished with sprinkles or other decorations immediately after glazing.
2 1/2 cups (12 1/2 ounces) unbleached all-purpose flour
3/4 cup (5 1/2 ounces) superfine sugar
16 tablespoons (1/2 pound, or 2 sticks) unsalted butter, cut into sixteen 1/2-inch pieces, at cool room temperature (about 65F)
2 teaspoons vanilla extract
2 tablespoons cream cheese, at room temperature
1 tablespoon cream cheese, at room temperature
3 tablespoons milk
1 1/2 cups (6 ounces) confectioner's sugar
For the cookies:
1. In bowl of standing mixer fitted with flat beater, mix flour, sugar, and salt on low speed until combined, about 5 seconds. With mixer running on low, add butter 1 piece at a time; continue to mix until mixture looks crumbly and slightly wet, about 1 minute longer. Add vanilla and cream cheese and mix on low until dough just begins to form large clumps, about 30 seconds.
2. Remove bowl from mixer; knead dough by hand in bowl for 2 to 3 turns to form large cohesive mass. Turn out dough onto countertop; divide in half, pat into two 4-inch disks, wrap each in plastic, and refrigerate until they begin to firm up, 20 to 30 minutes. (Can be refrigerated up to 3 days or frozen up to 2 weeks; defrost in refrigerator before using.)
3. Adjust oven rack to middle position; heat oven to 375F. Roll out 1 dough disk to even 1/8-inch thickness between 2 large sheets of parchment paper; slide dough on parchment onto baking sheet and chill until firm, about 10 minutes. Meanwhile, repeat with second disk.
4. Working with first portion of rolled dough, cut into desired shapes using cookie cutter(s) and place shapes on parchment-lined baking sheet, spacing them about 1 1/2 inches apart. Bake until light golden brown, about 10 minutes, rotating baking sheet halfway through baking time. Repeat with second portion of rolled dough. (Dough scraps can be patted together, chilled, and re-rolled once.) Cool cookies on wire rack to room temperature.
5. For the glaze: Whisk cream cheese and 2 tablespoons milk in medium bowl until combined and no lumps remain. Whisk in confectioner's sugar until smooth, adding remaining milk as needed until glaze is thin enough to spread easily. Drizzle or spread scant teaspoon glaze with back of spoon onto each cooled cookie, as desired.