Why not just call it "cheesy pull-apart garlic Eggplant"! - Low Carb Cheesy Pull-Apart Garlic 'Bread' made a little bit healthier using eggplant as a base and low fat grated mozzarella.
Use bunuelos and make cajeta buttercream or dulce de leche creama para Acer similar
I think this is ham stuffed eggplant. Either way, it looks awesome!