Step 1Heat the oven to 375 degrees. Butter a 13-by-9-inch oval baking dish with 1 tablespoon of the butter. Arrange the sliced squashes in the dish; set aside.
Step 2Heat a large skillet over medium-high heat. Add the remaining 2 tablespoons of butter and heat until melted. Add the onions and cook, stirring occasionally, until soft and caramel-colored, 8 to 10 minutes. Season with the salt and pepper. Stir in the chicken broth. Bring to a boil and pour over the squash.
Step 3Cover and bake 15 minutes, then uncover and continue to bake until the squash is tender, 30 minutes. Pour the whipping cream evenly over the top and bake until the top begins to brown, another 15 to 20 minutes. Sprinkle with the parsley before serving.