Cube the bread a day or two ahead and leave it out on the counter to dry, so it will fully absorb the flavors of the dressing. (If you forget, you can dry it in a 375° oven for a few minutes.) For a moister dressing, use the larger amount of broth. This makes a good main dish for vegans (use kosher rye, which excludes dairy). But it's good with sausage too; add about 1 pound, casings removed, browned and crumbled.
AT HOME (UP TO 1 DAY AHEAD)
Preheat oven to 375°. Toss squash with 1 tbsp. oil. Spread out on a baking sheet and roast until tender when pierced with a fork, about 15 minutes.
Meanwhile, heat remaining 2 tbsp. oil in a large frying pan. Cook onion, garlic, mushrooms, and celery, stirring often, until softened and starting to brown. Sprinkle with salt, then transfer to a large mixing bowl.
Add bread cubes, roasted squash, broth, and parsley; toss gently to combine. Transfer to a greased 9- by 13-in. baking dish.
AT THE PARTY
Bake at 350° until warm in the center and top is just toasted and crusty, about 1 hour.
*If you like a heartier flavor, use dark rye. Otherwise, use light rye, a mix of rye and sourdough, or all sourdough.
Servings Makes 16 cups
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.