In a large nonstick skillet, heat 2 Tbsp. of the oil over medium-high heat. Add eggplant and saute until very soft and browned, 12 to 15 min., stirring often. Transfer eggplant to a large bowl and mash with a potato masher until there are no large pieces and the texture is closer to mush. Mix in shallots, ½ cup of each cheese, Gourmet Santa Maria, and panko. Form into 12 to 15 meatballs (slightly larger than a ping pong ball). Set meatballs back in the bowl, cover, and refrigerate for 30 min. Preheat oven to 450 degrees. In the same skillet, heat remaining 2 Tbsp. oil over medium-high heat. Add meatballs and cook on all sides (assuming about 6 sides on a round meatball) until most of the exterior is nicely browned, 1 to 2 min. per side. To assemble: Slice hoagies lengthwise about three-quarters of the way through, so the hoagie still holds together. Remove a portion of the bread from inside and add a layer of sauce and basil leaves. Top with eggplant meatballs, more red sauce, and a generous portion of the remaining shredded cheeses. Place in the oven for 4 to 5 min. to melt the cheese and warm everything through. Serve hot.