• Place milk and eggs in a medium bowl and beat to combine. Tear bread into small pieces and stir into milk mixture. Let stand until milk is combined and bread is falling apart, about 5 minutes.
• In a large bowl, combine ground beef, grated onion, parmesan, parsley, salt, and pepper. Add soaked bread and use your hands to gently, but thoroughly, combine. Form the mixture into 1-1/2" balls, about the size of golf balls.
• Heat oil in a dutch oven or heavy-bottomed pot over medium-high heat. When shimmering hot, add half of the meatballs in a single layer and brown on all sides (they'll be cooked through later). Gently transfer to a plate, and repeat with remaining meatballs.

To make sauce:

• Wipe out the dutch oven with a paper towel and add remaining olive oil along with onion. Cook on medium heat until onion is soft and translucent, but not browning, about 6 minutes. Add garlic and cook until fragrant, about a minute more. Add tomatoes and bring to a boil. Puree the sauce with an immersion blender or with a regular blender (in batches, unless it has steam vents for pureeing hot foods). Return sauce to pot and gently add meatballs. Simmer over medium-low for about 25 minutes, until meatballs are cooked through and sauce thickens. Season to taste with salt, and stir in basil just before serving.
• Meanwhile, cook spaghetti in salted, boiling water until al dente according to package directions. Serve spaghetti topped with sauce and meatballs, with a showering of freshly grated parmesan.