Heat the olive oil in a large pot over medium-high. Brown the ground beef, breaking it up, about 8 minutes. Drain off the excess fat.
Add the onion and cook 5 minutes, then the garlic for 30 seconds. Stir in the tomato paste and cook 1 minute, until it darkens.
Add the crushed tomatoes, tomato sauce, oregano, basil, salt, red pepper flakes, and sugar. Simmer uncovered for 25 minutes, stirring occasionally, until thick.
Meanwhile, cook the lasagna noodles until just al dente, drain, and lay them flat on a sheet pan so they do not stick together.
Stir the ricotta, beaten egg, Parmesan, parsley, and salt together in a bowl. The egg is what sets the cheese layer so the lasagna slices cleanly.
Heat the oven to 375°F. Spread 1 cup of meat sauce across the bottom of a 9x13-inch baking dish.
Layer: 3 noodles, one third of the ricotta mixture, one quarter of the remaining sauce, and 1 cup of mozzarella. Repeat twice more, then finish with a final layer of noodles, the last of the sauce, and the remaining mozzarella.
Cover with foil (tent it so it does not touch the cheese) and bake for 45 minutes.
Remove the foil and bake 15 to 20 minutes more, until the top is bubbling and browned in spots.
Rest the lasagna on the counter for 25 minutes before cutting. This is what lets the layers set into clean slices.