Stir the baker's ammonia (ammonium carbonate) into the whole milk until dissolved; set aside.
In a large bowl, whisk together the all-purpose flour, fine sea salt, ground cinnamon, ground cloves, ground allspice, ground ginger, ground cardamom, ground white pepper, and ground anise.
In a stand mixer (or with a hand mixer), cream the unsalted butter and granulated sugar on medium speed until light and fluffy, 2–3 minutes.
Beat in the honey and unsulphured molasses until smooth, 1 minute.
Add the egg and lemon zest and beat until fully combined, 30–60 seconds.
Mix in half of the flour-spice mixture on low speed just until incorporated, then pour in the dissolved milk mixture and mix briefly. Add the remaining flour-spice mixture and mix until a soft, slightly tacky dough forms.
Scrape the dough into a bowl, cover, and chill until firm to scoop and the spices have bloomed, at least 12 hours and up to 24 hours.
Preheat the oven to 350°F (175°C) with a rack in the center. Line two baking sheets with parchment.
Scoop 1-teaspoon portions of dough (about 10–12 g), roll into smooth balls, and arrange 2 inches apart on the prepared sheets. Keep the remaining dough chilled as you work.
Bake one sheet at a time until the cookies are puffed, tops are cracked, and the bottoms are just turning golden, 12–14 minutes; the centers should feel set but not hard. Air out the kitchen, as baker's ammonia gives off an odor that dissipates after baking.
Let the cookies cool on the sheet for 5 minutes, then toss them in confectioners' sugar; after they cool completely, toss again to finish the coating. Store airtight at cool room temperature for up to 2 weeks (the flavor improves after a day).