Preheat oven to 350ºF.
Peel and slice eggplant and brush with olive oil.
Roast in oven for 20 minutes. Put half of eggplant aside; dice the other half and set aside.
Combine green onion, Parmesan, milk, yellow onion, basil, garlic, parsley, salt, pepper and one egg in a food processor and purée. When mixture is smooth, add 1/2 cup breadcrumbs and continue to purée until smooth. Add the half of the roasted eggplant that is not diced and purée.
Place mixture in a large bowl; add diced eggplant chunks and gently mix until combined.
Use an ice cream scoop or similar to form “meatballs.”
Place balls on a sheet tray; cover and refrigerate overnight.
Before cooking, combine remaining egg with 1 teaspoon water and mix. Add a pinch of salt and pepper to remaining 1 cup breadcrumbs. Coat the balls first in flour, then the egg wash, then finally the remaining seasoned breadcrumbs.
Heat 1 to 2 inches oil in a large, deep skillet over medium heat.
When oil shimmers, cook meatballs 2 to 4 minutes or until golden brown and cooked through.