In the bowl of a 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 food processor running, add molasses and milk; process until dough is evenly moistened and forms soft mass, about 10 seconds.
Divide dough in half and roll into ¼ inch thickness between two sheets of parchment paper. Place in refrigerator at least two hours (or overnight) or place in the freezer for 15 to 20 minutes, until firm.
Adjust oven racks to upper- and lower-middle positions and heat oven to 350 degrees. Line two cookie sheets with parchment paper.
Once firm, remove parchment from dough and cut out cookies using a 5-inch gingerbread man or 3-inch gingerbread cookies. Place on prepared baking sheets spacing cookies 1 inch apart. Bake until centers are just set and dough barely retains imprint when touched very gently with fingertip, 8 to 11 minutes. Rotating the baking sheets halfway through. Cool the cookies on the baking sheets about 2 minutes; using a wide metal spatula, transfer the cookies to a wire rack and cool to room temperature. Decorate as desired with royal icing.
Gather scraps; repeat rolling, cutting, and baking in steps 2 and 4. Repeat with remaining dough until all dough is used.