In a large pot over medium-low heat, sauté the olive oil, minced onions, and garlic until the onions are translucent, about 3 minutes.
Add the tomato paste, crushed tomatoes, salt, and pepper. Simmer covered for 30 minutes, stirring occasionally.
Preheat your oven to broil. Line a baking sheet with foil and lightly grease it with olive oil.
In a large bowl, combine the ground beef, eggs, breadcrumbs, Parmesan cheese, minced onion, salt, pepper, Italian seasonings, and garlic. Mix thoroughly with your hands.
Roll 1/3 cup of the mixture into a ball and place it on the prepared baking sheet. You should get around 14 to 15 meatballs.
Cook the meatballs in the oven's lower-middle position until browned, about 10-12 minutes. Flip and cook for an additional 2-3 minutes.
Add the meatballs to the tomato sauce. Simmer on low heat for at least 1 1/2 hours, stirring occasionally.
Adjust the sauce consistency with water if needed. Season with salt and pepper. Serve the meatballs with sauce, sliced basil, and Parmesan cheese.
Notes
For a twist, consider adding a dash of red pepper flakes to the tomato sauce for a spicy kick.