For bolder flavor, add 1/4 teaspoon red pepper flakes to the meat sauce and a pinch of nutmeg to the white sauce.
1.Dice carrot, 1-2 stalks celery, mushrooms, and garlic; transfer to bowl. Process tomatoes in food processor until almost (or half) smooth. Combine 1 teaspoon oil, onion, and pepper in Dutch oven. Cover and cook over medium-low heat until onion is softened, 3 to 4 minutes. Add carrot, celery, mushrooms, and garlic and cook, uncovered, until mushrooms release their liquid, 5 to 7 minutes. Increase heat to medium-high and cook until liquid has evaporated, 3 to 5 minutes. Then salt.
2. Add tomato paste and cook until paste begins to brown, about 2 minutes. Stir in turkey and 1 cup milk, using wooden spoon to break up any large chunks, and cook until most of milk has evaporated, 5 to 7 minutes. Stir in tomatoes, 1 cup broth, and bay leaf; bring to simmer and cook until sauce has thickened and most of liquid has evaporated, 45 to 60 minutes. Off heat, remove bay leaf, stir in basil, and season with salt and pepper.
3. Meanwhile, whisk remaining 1 cup milk, remaining 1 cup broth, and flour together in medium saucepan until smooth. Bring mixture to simmer over medium-high heat and cook, stirring constantly, until thickened, about 2 minutes. Off heat, stir in remaining 1 teaspoon oil and cheese. Season with salt and pepper.
4. Adjust oven rack to upper-middle position and heat oven to 425 degrees. Spread 2 cups meat sauce in 13 by 9-inch baking pan. Lay 3 noodles over sauce, leaving space between them. Repeat with 3 more layers sauce and noodles. Spread white sauce evenly over top layer of noodles, leaving 1-inch border around edge. Bake until lasagna is bubbling around edges and top begins to brown, 25 to 30 minutes. Cool on rack 20 minutes. Serve.
Make Ahead: You can make both the meat sauce and the white sauce up to 2 days in advance and refrigerate them until ready to use. Gently reheat the sauces separately before proceeding with step 4.
*I use the tomato paste that comes in a tube because it’s denser tasting and easy to store in fridge!