Heat the oven to 325 degrees F and arrange a rack in the middle. Coat a 10-inch spring form pan with butter. Set aside.
Whisk together flour, baking powder, cinnamon, salt and ground cloves in a large bowl to break up any lumps and aerate. Set aside. Whisk together honey, oil, coffee, sugar, and eggs in another large bowl until eggs are broken up and mixture is smooth and combined. Add dry mixture to wet and stir until combined.
Pour batter into the prepared pan and bake until golden brown and a toothpick inserted in the middle comes out completely clean, about 1 hour and 20 minutes. Remove from the oven, transfer to a rack and let cake cool in the pan for 10 minutes. Run a knife around the inside perimeter of the pan and remove the springform ring.
While the cake is cooling, add the butter to a large frying pan over medium-high heat. When the foaming subsides, add the figs cut side down. Cook undisturbed until browned, about 5 minutes.
Add the liqueur and honey, stir to coat the figs, and cook until the syrup is golden brown and the figs are soft but still intact, about 10 minutes. Top the cake with the fig mixture and serve.