Preheat oven to 450 F. Spray a large baking sheet with cooking spray and prepare a 9x13 casserole dish with cooking spray and set aside.
Spread the cubed butternut squash and chopped onion out on the baking sheet and toss with 3 tablespoons olive oil. Season with salt and pepper. Roast for approximately 20 to 25 minutes, or until squash is soft and turning golden-brown. Flip with a spatula half way through the baking time. When roasted, remove from oven and set aside. (You can do this step a day or two ahead of time, and refrigerate in an air-tight container.)Reduce oven temp to 375°. Meanwhile, bring the milk and rosemary to a simmer in a small sauce pan and keep warm. Do not boil.
In a larger saucepan, melt the butter with the garlic. Whisk in the flour and cook the roux, stirring for a few minutes over low heat. (This step lets the flour take on a nutty flavor and also helps to create a smooth texture once you start adding the liquid.)
Slowly whisk the milk mixture into the flour mixture, stirring to eliminate any lumps. Continue to simmer over low heat, whisking occasionally, until thickened. This will take about 7-10 minutes. Stir in the roasted squash and onions and stir well. Set aside. To assemble the lasagna, spoon about 1 1/2 cups of the butternut squash sauce in the bottom of the pan. Spread out. Lay three lasagna sheets lengthwise on top of the sauce. Use enough of a fourth piece to fill in the opening on the end. Spread half of the remaining sauce over the noodles and sprinkle with 1/2 cup of grated Parmesan. Repeat the process: noodles, sauce, Parmesan. Then finish with a layer of noodles on top. Mix ricotta and yogurt together in a bowl. Spread the ricotta-yogurt mixture evenly over the top of the noodles and cover generously with Parmesan cheese
Cover tightly with foil, (tent foil if needed so it doesn’t touch the top layer) and bake for 30 minutes. Remove foil and continue to bake for another 10-15 minutes, or until the top layer is bubbly and golden-brown. Remove from oven and allow lasagna to set up for about 10 minutes before cutting and serving.
Garnish each piece with a sprig of rosemary.