1. Cover potatoes with cold water, in a medium saucepan. Bring to a boil; add salt. Reduce heat to medium-high; cook potatoes until soft, about 25 minutes. In another medium saucepan, cover squash with cold water. Bring to a boil; add salt. Reduce heat to medium-high; cook until soft, 15 to 20 minutes. Drain potatoes and squash thoroughly.

2. Force potatoes through a ricer into a bowl. In a separate bowl, mash squash with a potato masher; stir in potatoes.

3. Bring 4 tablespoons butter and the cream to a simmer in a small saucepan over medium heat. Add 1/2 teaspoon salt and the nutmeg. Season with pepper. Stir cream mixture and 1/3 cup cheese into potato mixture. Season with salt and pepper, if desired. Spoon into a buttered 10-inch round baking dish.

4. Preheat oven to 350 degrees. Sprinkle mixture with crushed cookies and remaining cheese. Dot topping with remaining 2 tablespoons butter. Bake until topping is just browned, 20 to 30 minutes.