Brown the meat: Heat the olive oil in a large pot over medium heat and cook the onion for 4-5 minutes until soft. Add the ground beef and Italian sausage and cook for 8-10 minutes, breaking the meat apart, until no pink remains and both reach 160°F. Drain off the grease.
Bloom the garlic and paste: Stir in the garlic and tomato paste and cook for 1 minute, until the paste darkens and smells sweet instead of raw.
Simmer the sauce: Add the crushed tomatoes, tomato sauce, sugar, Italian seasoning, salt, black pepper, and red pepper flakes if using. Bring to a low simmer and cook uncovered for 30 minutes, stirring now and then, until the sauce is thick enough to mound on a spoon.
Boil the noodles: While the sauce simmers, cook the lasagna noodles in a separate pot of salted water for 1-2 minutes less than the package says. Drain and lay them flat on a sheet pan or a lightly oiled counter so they don't stick together.
Mix the ricotta filling: Stir together the ricotta, egg, parmesan, parsley, and 1/2 teaspoon salt in a bowl until smooth. The egg is what keeps the filling from running out the sides once it heats up.
Layer the pan: Spread 1 cup of sauce across the bottom of a 9x13 baking dish. Add 4 noodles, half the ricotta mixture, a third of the remaining sauce, and 1 cup of mozzarella. Repeat with 4 more noodles, the rest of the ricotta, another third of the sauce, and 1 cup of mozzarella. Finish with the last 4 noodles, the remaining sauce, and the last 2 cups of mozzarella.
Bake covered, then uncovered: Heat the oven to 375°F. Cover the dish with foil (spray the underside so it doesn't stick to the cheese) and bake for 25 minutes. Remove the foil and bake 20-25 minutes more, until the edges bubble and the top is golden and spotted brown.
Rest and slice: Let the lasagna sit for 15 minutes before cutting. Scatter fresh basil over the top and serve.
Notes
Simmer the meat sauce a full 30 minutes so it thickens enough to hold the layers, and rest the baked lasagna 15 minutes before cutting. Cook the ground beef and Italian sausage to an internal temperature of 160°F.