Preheat oven to 375 degrees. Cook lasagna noodles in a very large pot of salted, boiling water until just under al dente. Drain then return to the pot. Add a drizzle of extra virgin olive oil then gently stir to coat the noodles.
For the sausage:
Meanwhile, heat a large skillet over medium-high heat. Squeeze sausage out of its casing then break it up while it cooks. Remove to a plate and set aside.
For the Bechamel:
Turn the heat down to medium then, in the same skillet, melt butter. Add garlic then cook until fragrant, 30 seconds. Sprinkle in flour then whisk to combine and cook for 1 minute.
Slowly stream in chicken broth while whisking to avoid lumps. Add milk then whisk to combine. Season with salt and pepper.
Switch to a spatula then stir sauce until thick and bubbly, about 10 minutes. Pour bechamel into a bowl with a spout then set aside.
Assembly:
Spray a 9x13" baking dish with nonstick spray then add 1/4 cup bechamel to the bottom and spread into an even layer 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 layers 2 more times, for a total of three layers.
Cover baking dish with foil then bake for 25 minutes. Remove foil then bake for 15 more minutes, or until cheese is golden brown and sauce is bubbly. Let sit 10 minutes before slicing and serving.