Run a knife around edges of angel cake and turn it out onto a work surface. With a large serrated knife, cut cake horizontally into three equal layers, reserving top layer for another use or slicing it to grill along with panini. Place middle cake layer on a piece of foil large enough to hold it.
Peel bananas, leaving them lying in peel for ease of handling and slice thinly on bias. Pick up one banana with both hands, holding slices together, and place on cake, spreading slices to cover half of cake ring. Repeat with other banana so you have a cake ring topped with a ring of bananas. Sprinkle with dessert wine, if using, and top with bottom cake layer.
Use foil to cover the outside of a very heavy skillet, such as cast iron or enameled cast iron with a heat-proof handle. This will protect it from soot. Place skillet on grill and allow to heat on medium-high. When it's hot, add two tablespoons of the butter, spreading it with a spatula to coat skillet as it melts. Using your hands or two spatulas, carefully lift banana-filled panini into skillet. Use spatula to press edges firmly to give panini a uniform edge and re-adhere ragged pieces. Put a second heavy, heat-proof skillet on top of cake and press firmly to compact panini.
Close grill and let panini toast on medium to medium-high until golden brown and crisp. Check periodically by lifting the edge with a spatula. Depending on how hot your grill is and how heavy the skillet, the butter can start to burn. With two spatulas, remove panini to foil piece and melt the rest of the butter in skillet, spreading it around with spatula to coat skillet evenly.
Turn untoasted side of panini into skillet and return heavy skillet to the top, pressing again to compact. Toast until crisp and golden and bananas are soft - about another 10 minutes. Remove panini to a serving plate and serve in slices or on a bed of fresh seasonal fruit, if desired.