Preheat oven to 400 degrees.
In a large skillet over medium-high heat, heat the olive oil.
Add the onions, mushrooms, and garlic. Cook until soft and translucent. Add the thyme and basil.
Add the chicken and combine well.
Add the flour and stir until all of the flour is absorbed by the chicken mixture.
Add the cream and the chicken broth. Bring to a boil; stirring constantly.
Add the cheeses and spinach. Stir well to combine everything.
Spray a baking dish with cooking spray. (Recommend 9- x 13- inch)
Starting with the chicken mixture, assemble the lasagna in the baking dish, alternating between the chicken mixture and lasagna noodles.
Cover with foil and bake for 20 - 30 minutes.
Remove the foil, and broil for 5 additional minutes.
Remove from oven when done, and let stand 10 minutes before serving.