In a small bowl, combine the breadcrumbs and milk; set aside to soften for a few minutes.
Heat the butter and olive oil in a skillet over low heat. Add the chopped onion and sauté 10–15 minutes, until soft and lightly browned.
Place the ground chicken in a food processor. Add the soaked breadcrumbs (including any remaining milk), sautéed onion, egg, chopped parsley, minced garlic, salt, and pepper.
Pulse the mixture in the food processor just until evenly combined; do not over-process.
Pour enough vegetable oil into a large skillet to coat the bottom and heat over medium heat.
Scoop about 1/8 cup of the mixture for each meatball and roll into balls, wetting your hands if the mixture is sticky. Place meatballs in the hot oil in a single layer without crowding, working in batches if needed.
Cook the meatballs, turning as needed, until browned on all sides, about 10 minutes; they do not need to be fully cooked through at this stage.
Transfer browned meatballs to a plate lined with paper towels to drain any excess oil.
Wipe the skillet clean, return the meatballs to the skillet, and pour the jar of marinara sauce over them.
Cover the skillet with a tight lid and simmer on low heat 10–15 minutes, until the meatballs are cooked through.
Serve the meatballs hot, optionally garnished with grated Parmesan or chopped parsley.
