Sauté the aromatics. Heat the olive oil and butter in a large Dutch oven or stockpot over medium heat. Once the butter has melted, add the onion and cook for 3–4 minutes, until softened. Add the garlic and cook for another minute.
Make the creamy base. Sprinkle in the flour and whisk until combined. Cook for 2–3 minutes, stirring frequently. Slowly pour in the chicken broth, heavy cream, and milk, whisking continuously until smooth. Stir in the chicken bouillon, salt, pepper, onion powder, garlic powder, and paprika.
Add the pasta and vegetables. Stir in the broccoli, shredded carrots, and broken lasagna noodles. Increase the heat to medium-high and bring to a gentle boil.
Simmer. Reduce the heat to medium-low, cover, and simmer for about 15 minutes, stirring occasionally to prevent the noodles from sticking. Cook until the pasta is al dente and the vegetables are tender.
Add the cheese. Turn off the heat and gradually stir in the shredded cheddar until completely melted and the soup is creamy and smooth.
Serve. Taste and add more salt if needed. Ladle into bowls and serve warm.