Warm a deep large skillet over medium heat with 1 tablespoon olive oil. Once warm, add the chicken breaking it into small pieces with a wooden spoon and cook until about ½ way done, 5 minutes.
Add the diced onion and sauté it with the chicken for 5 minutes until softened and the chicken is just about cooked through.
Add in the 4 cloves of garlic and spices (1 teaspoon kosher salt, ½ teaspoon pepper, 1 teaspoon dried oregano, ½ teaspoon dried parsley, ½ teaspoon dried basil) and cook for 1-2 minutes until very fragrant.
Stir in the 2 tablespoon tomato paste until evenly distributed with the chicken/onion/garlic.
Stir in the 28oz tomato puree, 2 cups broth, and 1 tablespoon brown sugar until evenly combined with everything. Bring to a gentle simmer.
Carefully mix the 8oz raw broken lasagna noodles into the sauce until fully submerged.
Keep at a simmer, cover the dish and cook, stirring often, for about 20-30 minutes until the noodles are al dente. Add more chicken broth if needed.
Top with dollops of ricotta cheese and mozzarella cheese and broil until melted and golden. Serve warm with fresh basil.