Preheat oven to 350°F.
In a large bowl, whisk together the eggs and brown sugar until fluffy.
In a sifter over a medium bowl, measure flour, baking powder, salt, ground ginger, ground cinnamon, ground cloves, and ground nutmeg.
In a pan or pot, melt butter over medium-high heat until bubbly and golden brown. Add your fresh grated ginger and stir to combine. Remove from heat.
In a heat-proof bowl, measure molasses and baking soda. Add hot, nearly boiling coffee and whisk to combine.
Add your brown butter and ginger mixture to the hot molasses mixture and combine.
Alternate adding your sifted dry ingredients and your molasses / butter mixture to your eggs and brown sugar. Add 1/3 of each at a time and fold with a spatula.
Grease 6 ramekins with butter and place on a baking sheet. Fill each ramekin 1/2 - 2/3 of the way full with your gingerbread cake batter.
Bake for 25 - 30 minutes until cake tops spring back when pressed. Remove from oven and let cool slightly before running a knife around the edge of the cakes to loosen them. Remove from ramekins carefully.
In another bowl, whisk together powdered sugar, lemon juice, and a pinch of salt. Your glaze should be slightly on the runny side.
On a wire rack over a plastic-wrap-lined pan, pour your glaze over the warm cakes to coat the tops evenly.
Slice your lemon in thin, 1/8" rings. Remove seeds.
In a deep sauté-pan, heat water and white sugar over medium-high heat. Stir once to combine and then don't disturb.
Once the sugar mixture begins to boil rapidly, turn heat down to a gentle simmer and add your lemon slices. Cook for 25-30 minutes total, flipping to coat each side.
Carefully remove your lemon slices and place on a parchment or silicon-lined baking sheet. Let cool for 30 minutes - 1 hour before garnishing each ginger cake with a candied lemon slice.