Put honey, molasses, and butter into a small pot and cook over medium-low heat, stirring constantly, until hot, 2–3 minutes. Remove from heat and let cool. Add eggs and whisk to combine. Put flour, half the lemon peel, almonds, cinnamon, pepper, cloves, cardamom, and baking powder into a large bowl and stir to combine. Add honey mixture and beat with a wooden spoon until well combined, to form a dough. Cover surface of dough with plastic wrap and refrigerate for 8 hours or overnight.
Preheat oven to 350°. Line 2 baking sheets with parchment paper and set aside. Lightly oil your palms with some of the oil. Form dough into 36 balls, each about 1" wide (the dough will be very sticky, so keep your hands lightly oiled while working). Divide dough balls between baking sheets, keeping them spaced 1" apart. Bake until slightly cracked on top and just firm to the touch, about 15 minutes. Transfer cookies to a wire rack and let cool slightly.
Meanwhile, whisk together confectioners' sugar, rum, and 5 tsp. hot water to make a smooth glaze. While cookies are still warm, use a pastry brush to coat each one with a layer of glaze. While the surfaces of the cookies are still moist with glaze, garnish each top with pieces of the remaining lemon peel. Set cookies aside to let cool completely. Eat right away or store in an airtight container, layered between sheets of waxed paper, for up to one week.