Preheat oven to 375 degrees. Cook lasagna noodles in a very large pot of salted, boiling water until just under al dente. Drain and return to the pot. Add a splash of extra virgin olive oil and gently stir to coat the noodles.
Meanwhile, heat a large skillet over medium heat. Squeeze sausage out of its casing and cook while breaking up until no longer pink. Remove to a plate and set aside.
In the same skillet, melt butter, then add garlic and cook until fragrant, about 30 seconds. Sprinkle in flour, then whisk to combine and cook for 30 more seconds.
Slowly pour in chicken broth a few Tablespoons at a time, whisking to break up any lumps. Continue pouring and whisking until mixture is smooth. Pour in milk and whisk to combine. Season with salt & pepper.
Switch to a spatula and stir sauce until thick and bubbly, about 10 minutes. Pour into a bowl with a spout, and set aside.
Spray the bottom and sides of a 9×13″ baking dish with non-stick spray. Pour 1/4 cup sauce into the bottom, then spread evenly with a spatula. Place 3 lasagna noodles in the bottom, then top with 1/3 of the tomatoes, 1/4 cup torn basil, 1/3 of the cooked turkey sausage, 1/2 cup mozzarella cheese, and 1/3 of the remaining sauce. Repeat 2 more times, for a total of three layers.
Cover baking dish with foil and bake for 25 minutes. Remove foil and bake for 15 more minutes, or until cheese is golden brown and sauce is bubbly. Let sit 5 minutes before slicing and serving.
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