In food processor fitted with steel blade, process flour, sugar, cinnamon, ginger, cloves, salt and baking soda until combined, about 10 seconds.
Scatter butter pieces over flour mixture and process until mixture is sandy and resembles very fine meal, about 15 seconds.
With machine running, gradually add molasses and milk; process until dough is evenly moistened and forms soft mass, about 10 seconds. (Alternatively, in the bowl of a standing mixer fitted with paddle attachment, stir together flour, sugar, cinnamon, ginger, cloves, salt and baking soda at low speed until combined, about 30 seconds. Stop mixer and add butter pieces; mix at medium-low speed until mixture is sandy and resembles fine meal, about 1½ minutes. Reduce speed to low and, with mixer running, gradually add molasses and milk; mix until dough is evenly moistened, about 20 seconds. Increase speed to medium and mix until thoroughly combined, about 10 seconds.).
Scrape dough onto work surface; divide in half. Working with one portion of dough at a time, roll to ¼-inch thick between two large sheets of parchment paper. Leaving dough sandwiched between parchment layers, stack on cookie sheet and freeze until firm, 15 to 20 minutes. (Alternatively, refrigerate dough 2 hours or overnight.).
Preheat oven to 350 degrees F. Line two cookie sheets with parchment paper.
Remove one dough sheet from freezer; place on work surface. Peel off top parchment sheet and lay it back in place. Flip dough over; peel off and discard second parchment layer. Cut dough into gingerbread people or round cookies, transferring shapes to parchment-line cookie sheets with a wide metal spatula, spacing them ¾-inch apart. Repeat with remaining dough until cookie sheets are full. Bake cookies until set in centers and dough barely retains imprint when touched very gently with fingertip, 8 to 11 minutes, rotating cookie sheet from front to back halfway through baking time. Do not overbake. Cool cookies on sheets 2 minutes, then remove with wide metal spatula to wire rack; cool to room temperature.
Gather scraps; repeat rolling, cutting and baking from steps 2 and 4. Repeat with remaining dough until all dough is used.
Once cookies are cool, decorate with royal icing, if desired. Store in an airtight container at room temperature for up to 1 week.