Brown the beef: Heat the olive oil in a large pot over medium-high heat. Add the onion and cook for 5 minutes until softened. Add the ground beef and cook for 6-8 minutes, breaking it up as it browns, until no pink remains and it reaches 160°F. Drain off the excess grease.

Build the sauce: Stir in the garlic and tomato paste and cook for 1 minute until the paste darkens. Add the crushed tomatoes, oregano, 1 1/2 teaspoons of the salt, the pepper, and the red pepper flakes if using. Simmer uncovered for 15 minutes, stirring occasionally, until slightly thickened.

Undercook the pasta: While the sauce simmers, boil the ziti in well-salted water for 2-3 minutes less than the package says for al dente. It should still be noticeably firm in the center. Drain and return it to the empty pot.

Mix the ricotta: Heat the oven to 375°F. In a bowl, stir together the ricotta, egg, 1/4 cup of the pecorino, and the remaining 1/2 teaspoon salt until smooth.

Toss everything together: Add about three-quarters of the sauce and all of the ricotta mixture to the drained pasta and stir until every tube is coated and the ricotta has streaked through. Fold in the cubed mozzarella.

Assemble the pan: Spread a thin layer of the remaining sauce across the bottom of a greased 9x13-inch baking dish. Add the pasta mixture and spread it level, then spoon the last of the sauce over the top and scatter on the shredded mozzarella and remaining 1/4 cup pecorino.

Bake covered, then uncovered: Cover tightly with foil and bake for 20 minutes, then remove the foil and bake another 15-20 minutes, until the cheese is bubbling and browned in spots.

Rest and serve: Let the pan rest for 10 minutes so it sets up enough to cut clean squares, then scatter the fresh basil over the top.