Preheat oven to 350°F. Line a baking sheet with parchment paper. Fill a small, wide bowl or plate with powdered sugar. Set the powdered sugar and a glass with a wide flat bottom nearby in preparation for pressing the cookie dough.

Roll each pre-cut square of cookie dough into a ball and spread on baking sheet about 2 inches apart. While your hands are still slightly buttery from rolling, lightly coat the bottom of the glass to help the powdered sugar stick on the first use. For each dough ball, dip the bottom of the glass into the powdered sugar, then press the dough ball to about ¼ inch thickness.

Bake 16-20 minutes or until just before browning. Bake just until edges lose their sheen for the softest, most sandwich-friendly texture. Remove baking sheet from the oven, tap on a flat surface if cookies are puffy. Without waiting, use a small cookie cutter to cut out a shape from half of the cookies. Cut slightly off-center so the prettiest part of the frosting shows through after assembly. Transfer cookies to a cooling rack and allow to cool completely.

Prepare the frosting while cookies cool. Prepare 1 cup each of two flavored or colored frostings as outlined below. If using straight from container, skip ahead to “Assemble Piping Bags”.

Cut 2 (8 inch) pieces of plastic wrap and lay them out on a flat surface. On each, spread 1 cup of frosting in a line. Fold one side of plastic wrap snuggly over frosting lengthwise. Then fold other side of plastic wrap over frosting and seal into a roll. Repeat with second frosting color or flavor.

Lay both rolls of frosting beside each other with frosting aligned on one end. Trim one end of each frosting roll close to the frosting line before inserting into the piping bag. Once both are in the piping bag, squeeze evenly on both sides until both colors appear when piped.

Assemble Cookie Sandwiches

Once cookies have cooled completely, match top and bottom pieces together according to size. Lay pairs out next to each other with the bottom flipped over. Starting just off-center, hold the piping bag vertically and pipe a smooth spiral from center outward. Try not to press down when piping. Allow the frosting to flow (like a string) behind the piping tip and drop to the cookie naturally. At the edge, stop squeezing the piping bag but continue to move around the outer edge until the frosting breaks off neatly.

Optionally, allow frosting to set in refrigerator for up to 10 minutes before sandwiching. Align cut out cookie with the best part of the swirled frosting and place down gently with just a small press. Optionally, allow frosting to set even further in refrigerator for 30-60 minutes. Remove from refrigerator at least 10 minutes before serving to soften cookies up again.