Make the sauce: Warm the olive oil in a large skillet over medium heat. Add onion and cook until softened, 4–5 minutes. Stir in garlic for 30 seconds, then add the ground beef. Cook, breaking it apart, until no pink remains, 5–6 minutes; drain excess fat if needed.
Stir in tomato paste and cook 1 minute to caramelize. Add crushed tomatoes, 1 teaspoon Italian seasoning, red pepper flakes, and 1/2 teaspoon kosher salt. Bring to a gentle simmer, then reduce heat to low and cook, partially covered, for 12–15 minutes to thicken and meld.
While the sauce simmers, bring a large pot of well-salted water to a boil. Cook the jumbo shells 1 minute less than package directions so they stay sturdy when filled. Drain, rinse briefly under cool water, and set spaced apart on a parchment-lined tray to prevent sticking. Tip: Slightly undercooking the shells helps them hold their shape during stuffing and baking.
Heat the oven to 375°F and lightly oil a 9×13-inch (3-quart) baking dish.
Mix the filling: In a medium bowl, combine ricotta, egg, 3/4 cup mozzarella, 1/3 cup Parmesan, 1/2 teaspoon Italian seasoning, and 1/4 teaspoon kosher salt until smooth and thick.
Assemble: Spread about 1 cup of the beefy tomato sauce over the bottom of the baking dish. Spoon or scoop the ricotta mixture into the shells (a small cookie scoop works great) and nestle them into the sauce. Spoon the remaining sauce over and around the shells. If your sauce is very thick, splash 2 tablespoons water around the edges for steam.
Top and bake: Sprinkle the shells with the remaining 1 cup mozzarella and 1/3 cup Parmesan. Cover tightly with foil and bake for 20–22 minutes, until the sauce is bubbling. Uncover and broil 2–3 minutes, watching closely, until the cheese is spotty and golden.
Rest 5 minutes so the filling sets, then shower with chopped basil and serve warm.