Start by heating one tablespoon of olive oil in a large pot over medium heat. Add diced chicken and cook until lightly browned and almost cooked through. Remove the chicken and set aside. This locks in the juices while allowing the chicken to finish cooking later in the broth.
Add the remaining olive oil and butter to the pot and melt together. Toss in the onions, carrots, and bell peppers. Sauté for about 3-4 minutes until the veggies are softened. Add the minced garlic and cook for another minute, letting its aroma fill the kitchen.
Sprinkle the flour over the vegetables and stir continuously for 2 minutes. This ensures the flour cooks and doesn't leave a raw taste.
Gradually pour in the chicken broth while stirring to prevent lumps. Add the cooked chicken back into the pot, along with the broken lasagna noodles. Simmer everything for 10-15 minutes or until the noodles are perfectly tender.
Reduce the heat to low and stir in the half and half, heavy cream (if using), and chopped spinach. Cook until the spinach is wilted and the soup is warmed through.
Remove the soup from the heat and mix in freshly grated Parmesan cheese. Stir well until the cheese is melted and the soup reaches its velvety consistency.