In a large pot of salted boiling water, add spaghetti and cook until al dente, about 8 minutes. Drain water then return the spaghetti to the pot. Add 1 egg and theParmesan and toss to combine.
Meanwhile, make sauce. In a large pot over medium, heat olive oil. Add onion and cook until tender, about 5 minutes. Stir in garlic and cook until fragrant, about 30 seconds. Add the ground beef, breaking up the meat with a wooden spoon, and cook until the meat is no longer pink, about 6 minutes. Drain fat then return the pot to medium heat and stir in tomato paste. Cook for 1 minute, then add the canned tomatoes and oregano. Season with salt and pepper and simmer for 10 minutes.
In a medium bowl, combine Mozzarella and remaining egg. Stir to combine.