Bring a large pot of water to a vigorous boil. Add 1 tablespoon olive oil, 1 teaspoon salt, and the lasagna noodles. Cook for the amount of time indicated on the package for al dente. Rinse the cooked noodles with cool water until cool enough to handle. Drain well and transfer them to a large sheet of foil to prevent them from sticking together.
In a large skillet, melt the butter with the remaining 2 tablespoons of olive oil over MEDIUM heat until melted. Add the garlic and cook, stirring, for a minute or two. Sprinkle the flour over the top and whisk until well incorporated. Slowly add the milk, whisking until smooth. Slowly add the chicken broth, whisking as you add it. Season with 1 teaspoon basil, ½ teaspoon oregano, ½ teaspoon thyme, and ½ teaspoon salt. Increase the heat, if needed, to bring it to the point of a low simmer (don’t boil). Continue to cook, whisking occasionally, for about 3 minutes or until thickened. It should be thickened, but pourable - similar to marinara sauce consistency. Remove from the heat and add the spinach, mixing to incorporate it with the sauce just until it wilts. Set aside.
In a large bowl, combine the ricotta cheese, sour cream, egg, chicken, remaining 1 teaspoon basil, ½ teaspoon oregano, ½ teaspoon thyme, ½ teaspoon salt and black pepper and mix until smooth. Fold in ½ cup of the mozzarella (reserve remaining for layers) and all of the Parmesan cheese. Set aside.
Set the oven rack to the center position and preheat the oven to 350 degrees F.
Spoon about ½ cup of the spinach white sauce into a 13- x 9-inch baking dish and spread it out across the bottom. It won’t be a thick layer, just enough to barely cover the bottom of the dish.
Layer #1 - Lay 3 of the lasagna noodles over the sauce, edge to edge. Spoon half of the chicken ricotta mixture over the noodles.
Layer # 2 - Lay 3 lasagna noodles over the chicken ricotta mixture. Spoon ⅓ of the spinach white sauce on to the noodles and use a spoon to spread it out (light layer). Sprinkle 1 cup of mozzarella over the sauce.
Layer #3 - Add 3 lasagna noodles and top with remaining half of the chicken ricotta mixture.
Layers #4 and #5 - Lay 3 cooked lasagna noodles over the chicken ricotta mixture. Spoon ⅓ of the remaining spinach white sauce over the noodles and spread it out. Sprinkle 1 cup of shredded mozzarella over the top. This is repeated once more for the 5th and final layer, ending with all of the remaining spinach white sauce and mozzarella cheese.
Coat the underside of a large sheet of foil with nonstick cooking spray and place it, coated side down, over the lasagna, lightly crimping the edges.
Transfer the baking dish to the oven and bake for 40 minutes. Remove the foil, and bake for an additional 15 minutes or until hot and bubbly. Set the oven to BROIL and cook until the top is just lightly browned, about 2 to 3 minutes (rotate the baking dish, if needed, for even browning).
Let lasagna rest for about 10 minutes before slicing and serving. Can garnish with torn fresh basil, if desired.
