Combine white and brown sugars in a saucepan with honey, water, cinnamon, ginger, cardamom, nutmeg, allspice, cloves, and cayenne pepper. Place over medium heat and whisk until the sugars dissolve and it just starts to simmer, 1 to 2 minutes. Immediately remove from the heat and let cool for 4 to 5 minutes.
Add salt, baking soda, heavy cream, and egg and whisk until thoroughly combined. Add flour and stir together with a wooden spoon until everything comes together as a dough.
Transfer dough to a piece of plastic wrap. Press into a ball and wrap tightly. Place in the refrigerator and let rest for 1 to 2 days.
When ready to bake, preheat the oven to 375 degrees F (190 degrees C). Line 2 baking sheets with parchment paper.
Remove dough from the refrigerator and scoop into rounded teaspoons. Roll each one into a smooth ball if desired, and place on a prepared baking sheet.
Bake in the center of the preheated oven until cookies are perfectly dome-shaped with light golden brown bottoms, 9 to 10 minutes; don't overbake. Let cool on the pan all the way down to room temperature, 20 to 30 minutes.
While the cookies are cooling, repeat Steps 5 and 6 to shape and bake the remaining cookies.
Make icing by placing powdered sugar in a bowl. Stir in lemon juice, a few teaspoons at a time, until icing is very thick, but still slightly runny.
Dip the top of each cooled cookie into the icing. Let it drip, then flip it over and place on a wire rack set over a piece of parchment paper and let harden.