Step 1In a large bowl, combine the brown sugar, butter, cinnamon, ginger, nutmeg, cloves, coriander, salt and baking soda. Use a Microplane grater to finely grate the zest off of two lemons into the bowl; reserve the lemons. Beat the mixture with an electric mixer on medium-low speed until smooth, about 2 minutes (see Baker’s Note). Add half the flour and beat on low speed until almost combined. With the mixer on low speed, pour in the milk, then immediately add the remaining flour and continue mixing until just combined. Split the dough in half and shape each into a ½-inch-thick disk. Wrap each separately in plastic wrap and refrigerate until firm, at least 15 minutes or up to overnight.
Step 2Heat the oven to 350 degrees. Line 2 baking sheets with parchment paper.
Step 3Unwrap 1 disk and transfer to a lightly floured work surface. Use a rolling pin to flatten the dough until 3/16-inch thick, then cut out shapes using palm tree, cactus and monstera leaf cutters (see note above), dusting the cutters with more flour between each use to keep them from sticking to the dough. Use the tip of a paring knife or a cotton swab to press through the more intricate parts of the cutters so the dough shapes come out easily, and use a flat metal spatula to transfer the cut shapes to the baking sheets, spacing 1 inch apart. Reroll and flatten scraps as many times as you can until no more dough is left.
Step 4Bake, rotating sheets from front to back and top to bottom halfway through, until cookies are set and dry to the touch, about 16 minutes. Let the cookies cool on the baking sheets for 1 minute before transferring to a wire rack to cool completely. Repeat with the remaining dough disk to make more cookies.
Step 5To make the glaze, juice all three lemons, measure out 6 tablespoons and pour into a wide shallow bowl; reserve any remaining. Add the powdered sugar to the juice and stir until it forms a thick but pourable glaze, thinning it out with more juice, if necessary. Spread the sanding sugar over the bottom of another wide shallow bowl.
Step 6Dip the top of each monstera leaf and cactus cookie in the glaze to coat completely then lift to let the excess drain; for the palm trees, just dip the leaves section, leaving the trunk bare. Immediately place the glazed side of the cookie in the sanding sugar and press lightly to ensure the sugar evenly covers the glaze. Invert the cookies onto a wire rack and immediately press in sugar snowflakes over the cookies. Let the cookies stand until the glaze sets firm, at least 20 minutes.