Heat olive oil in a 5–6 quart Dutch oven over medium-high heat until shimmering; add the ground meat and cook, breaking into small pieces, until browned and no longer pink, about 6–8 minutes, then drain excess fat if more than 1 tablespoon remains.

Reduce heat to medium and add the diced onion and minced garlic; sauté until the onion is translucent, about 4 minutes.

Stir in tomato paste and cook 1 minute, then add the chicken broth, crushed tomatoes, diced tomatoes with juices, oregano, basil, red pepper flakes if using, and kosher salt; bring to a gentle simmer and cook uncovered for 10 minutes.

Break the lasagna noodles into 2–3 inch pieces and add to the simmering broth; simmer gently until the noodles are tender but not mushy, about 8–10 minutes, stirring occasionally and adding up to 1/2 cup extra broth if the soup becomes too thick.

In a small bowl, mix ricotta, grated Parmesan, black pepper, and chopped basil; remove the pot from heat and wait 30 seconds, then stir the ricotta mixture into the soup gently so it ribbons through, sprinkle shredded mozzarella on top, cover and let sit 5 minutes to melt, then serve with extra cheese if desired.