Preheat oven to 350 degrees. Place lasagna noodles in a 9×13 pan. Fill pan with hot water and a drizzle of olive oil and let noodles soak while preparing the other ingredients (omit this step if using oven-ready lasagna noodles).

In a large saucepan, whisk together chicken broth, flour, thyme and 1/4 teaspoon each of basil and oregano. Bring to a boil over medium-high heat, stirring constantly. Reduce heat and allow sauce to simmer and thicken while preparing chicken and vegetables.

Heat olive oil in a large skillet over medium-high heat. Add cubed chicken, remaining 1/4 teaspoon each of basil and oregano, and salt and pepper to taste. Saute until chicken is cooked through, about 5 minutes. Transfer chicken to a plate.

In the same skillet, melt the butter, then add the chopped onion, garlic and carrots. Cook and stir until vegetables are tender. Add the chopped tomatoes and frozen spinach and cook until heated through. Return chicken to skillet with vegetables.

Spread a scant cup of the thickened chicken broth in the bottom of a greased 9×13 inch baking dish. Top with a layer of noodles. Spread 1/3 of chicken and vegetable mixture over noodles. Top with 1/3 of the thickened broth (about 2 cups), followed by 1/3 of the mozzarella cheese. Repeat twice, ending with a layer of mozzarella cheese. Top with 1/2 cup Parmesan cheese. Bake, uncovered, for about 45 minutes, until lasagna is bubbly and cheese is golden brown. Let rest 10 minutes before serving.