Bring a kettle of water to a boil. Fill a mug with boiling water, let it sit for 30 minutes, and then discard the water.
Meanwhile, crush the nutmeg and cinnamon stick with a rolling pin or heavy skillet. Put the nutmeg, cinnamon, ginger, cloves, and 1 cup water in a small, heavy saucepan (preferably one with a pour spout) over medium heat. Simmer until the spices have lightly infused the water, about 5 minutes. Remove the spices with a slotted spoon and discard.
Add the honey and the lemon juice to the infused water. Stir until the honey is completely dissolved. Add the Becherovka and Fernet Branca, heat just until the mixture begins to steam, then pour into the pre-warmed mug. Taste and adjust the seasoning with more honey, lemon juice, or water. Serve hot.
