Heat the oil in a high-sided, large skillet over medium. Add the butternut squash and cook, stirring occasionally, until the squash is golden brown and starting to soften, 2 to 3 minutes.
Stir in the onion and season with ½ teaspoon salt and cook until the onion is softened, another 2 to 3 minutes.
Push the veggies to one side of the skillet and add the ground turkey. Using a spoon or meat chopper, break the meat up into crumbles until the turkey is cooked through. About 7 minutes. Once the turkey is mostly cooked through, stir it in with the onions and butternut squash. The turkey will finish cooking with the rest of the ingredients.
Add in garlic, thyme, sage, remaining salt, and pepper. Cook for 1 minute or until garlic is fragrant.
Stir in the broken lasagna noodles then add the broth and milk, making sure the noodles are just covered with the liquid.
Simmer, stirring every few minutes, until the noodles are cooked through, about 15 minutes. Taste and add more salt and pepper as needed.
Add the ¾ mozzarella and the parmesan cheese, stirring everything together until fully melted.
Dollop the ricotta over the top, if using, then sprinkle with the remaining mozzarella. Cover the top of the pan to melt the cheese or place under the broiler until the cheese is bubbling and brown.
Garnish with herbs, if desired, then serve.