Dice onion, mince garlic, remove sausage from casings, break lasagna noodles into 2-inch pieces, and measure all seasonings.
Heat olive oil in a large Dutch oven over medium-high heat. Brown ground beef and Italian sausage for 7-10 minutes, breaking into crumbles, until no pink remains. Remove excess fat if needed.
Reduce heat to medium. Add diced onion and cook 4-5 minutes until softened. Add garlic and red pepper flakes, stirring constantly for 60 seconds until fragrant.
Push meat to the sides, add tomato paste to the center, and cook 60-90 seconds until darkened. Stir to coat everything evenly.
Add crushed tomatoes, diced tomatoes with juices, chicken broth, oregano, basil, Italian seasoning, salt, and pepper. Stir and scrape up browned bits from the bottom.
Bring to a boil, then reduce to medium-low and simmer uncovered for 15 minutes.
While soup simmers, boil lasagna noodles in salted water for 2 minutes less than package instructions. Drain and toss with a drizzle of olive oil.
In a small bowl, combine ricotta, 3/4 cup mozzarella, and 1/4 cup Parmesan with a pinch of salt and pepper. Set aside.
Add cooked noodles to the simmering soup and stir gently. Simmer 2-3 more minutes. Taste and adjust seasoning.
Ladle into bowls, top with a generous dollop of the cheese mixture, sprinkle remaining mozzarella and Parmesan, and garnish with fresh herbs. Serve immediately.