Heat oil in 12-inch skillet over medium-high heat until shimmering. Add onions, tomato paste, garlic, oregano and red pepper flakes and cook until onions are softened and lightly browned, 8-10 minutes.
Transfer half of onion mixture to large bowl; set aside. Stir wine into skillet with remaining onion mixture and scrape up any browned bites; transfer to slow cooker. Stir tomatoes, water, and soy sauce into slow cooker.
Add bread and milk to bowl of onion mixture and mash to paste with fork. Mix in ground beef, sausage, Parmesan, parsley, egg yolks, 3/4 tsp salt, 1/2 tsp pepper using hands. Pinch off and roll mixture into 1.5 inch meatballs (about 18 meatballs total).
Microwave meatballs on large plate until fat renders and meatballs are firm, 5-7 minutes. Nestle meatballs into slow cooker, discarding rendered fat. Cover and cook until meatballs are tender, 4-6 hours on low.
Let meatballs and sauce settle for 5 minutes, then remove fat from surface using large spoon. Gently stir in basil and sugar, season with salt, pepper and sugar to taste, and serve.