Preheat the oven to 400°F.
Arrange the squash in a single layer on a sheet pan covered with parchment paper. Drizzle with olive oil and season with salt and pepper. Place in the oven and roast until cooked through, about 20-25 minutes.
While squash is baking, melt the butter in a saucepan. Add the garlic and one teaspoon of Herbs de Provence to the butter. Add flour to the mixture and whisk until flour turns pale blond in color. Add the milk and whisk to combine. Add the cream cheese and whisk until incorporated. Season with salt and pepper to taste.
To assemble, spread a layer of white sauce on the bottom of a deep lasagna baking dish and top with a layer of noodles. In the following order, layer butternut squash rings, ⅓ cup cottage cheese (dropped by the spoonful), ⅓ Havarti, ¼ of the Gruyère and a thin layer of white sauce. Top with noodles and repeat the layering process two more times. Top the last layer of noodles with remaining sauce and shredded Gruyère. Sprinkle with the remaining Herbs de Provence.
Cover and bake for 45 minutes.
Uncover and bake 15 minutes longer until brown and bubbly. Let stand 5-10 minutes before eating.