Make the Tomato Sauce - In a large pot or Dutch oven, heat olive oil over medium-low heat. Once hot, add the onion and garlic, and sauté until the onions are translucent, about 3 minutes.Stir in the tomato paste and cook for 1 minute. Stir in the crushed tomatoes, salt, and pepper. Simmer covered, with lid slightly ajar to prevent splattering for 30 minutes, stirring occasionally. Season with salt and pepper to taste.
Heat the Oven - Set the oven rack to the lower-middle position. Heat the oven to broil. Line a large baking sheet with foil and lightly grease it with olive oil. Set aside.
Make the Meatball Mixture - In a large bowl, add the ground beef, eggs, breadcrumbs, parmesan cheese, minced onion, salt, black pepper, Italian seasoning, and minced garlic. Use your hands to mix thoroughly until combined.
Shape the Meatballs - Measure out 1/3 cup of the ground beef mixture (3 ounces), about the size of an egg, then roll it into a ball. Evenly space them on the prepared baking sheet. This should yield 14 to 15 meatballs.
Broil the Meatballs - Transfer the meatballs to the lower-middle position in the oven. Cook until the surface is browned, about 10 to 12 minutes. Flip the meatballs and cook for an additional 2 to 3 minutes to lightly brown the other side.
Simmer - Transfer the meatballs to the tomato sauce. Cover the pot with the lid slightly ajar, and simmer on low heat for at least 1 ½ hours, checking and stirring every 20 minutes, or as needed. The meatballs should be fork-tender when sliced.
To Serve - If needed, adjust the consistency of the sauce with water, about 1 tablespoon at a time. Season to taste with salt and pepper. Serve meatballs topped with sauce, sliced basil, and Parmesan cheese if desired.