In a large Dutch oven or pot, melt butter and olive oil over medium heat. Add the onion, carrots, and celery and cook for 5-7 minutes, until softened. Stir in the minced garlic and cook for 1 minute more until fragrant.

Sprinkle the flour over the vegetables and stir for 1 minute. Slowly whisk in the chicken broth until smooth. Add the Italian seasoning, salt, and pepper. Bring to a simmer.

Add the broken lasagna noodles and shredded chicken to the pot. Continue to simmer for 10-12 minutes, or until the noodles are al dente, stirring occasionally to prevent sticking.

While the noodles cook, whisk together the ricotta cheese and heavy cream in a medium bowl until smooth. Slowly ladle about 1 cup of the hot soup broth into the ricotta mixture, whisking constantly until combined. This prevents the cheese from curdling.

Reduce the pot's heat to low. Stir the tempered ricotta mixture into the soup. Add the shredded mozzarella and grated Parmesan cheese, stirring gently until the cheeses are completely melted and the soup is creamy. Do not let it boil.

Ladle the hot soup into bowls and garnish with fresh parsley. Serve immediately.