Chop the onion and mince the garlic, break the lasagna noodles into 2–3 inch pieces, and measure tomatoes and broth so everything is ready.

Heat 1 tablespoon olive oil in a 5- or 6-quart Dutch oven over medium-high heat until shimmering, then add 1 pound ground beef and cook, breaking up the meat, about 6–8 minutes until browned; remove meat with a slotted spoon and set aside, leaving about 1 tablespoon fat.

Add the diced onion and cook until soft and starting to color, about 5 minutes, then stir in garlic and cook 30 seconds; return the browned meat and stir in 1 tablespoon tomato paste, cooking 1–2 minutes.

Add 3 cups crushed tomatoes and 3 cups low-sodium broth, scrape up browned bits, then add 1 teaspoon dried oregano, 1/2 teaspoon dried basil, 1/2 teaspoon red pepper flakes (optional), and 1 teaspoon kosher salt; bring to a gentle simmer and cook uncovered for 10 minutes.

Add the broken lasagna noodles and the browned meat back to the pot, stirring and simmering gently for 8–10 minutes until the pasta is tender but not falling apart, adding up to 1/2 cup additional broth if the soup becomes too thick.

While the pasta cooks, whisk together 1 cup ricotta, 1 large egg, and 1/3 cup grated Parmesan until smooth; remove the pot from heat and let cool 60–90 seconds, then temper the ricotta mixture with two spoonfuls of hot soup before stirring it back into the pot to avoid curdling.

Taste and adjust seasoning, serve topped with extra Parmesan and chopped fresh basil or parsley.