Combine 2 1/2 pounds whole unpeeled beets and 1 large unpeeled russet potato in a pot; cover with cold water. Bring to a boil and cook until soft, about 45 minutes; drain. Peel the beets and potato and puree with 3 tablespoons butter; season with salt. Top with horseradish sauce.

Peel and roughly chop 3 pounds celery root. Place in a pot and cover with equal parts milk and water (about 2 1/2 cups each); add a pinch of salt. Bring to a simmer and cook until soft, 20 to 25 minutes; drain. Puree with 1/3 cup heavy cream and 2 tablespoons butter. Season with salt, then add 2 tablespoons whole-grain mustard and pulse to combine.

Halve 1 large unpeeled butternut squash (about 3 pounds) and cut into thick wedges, discarding the seeds. Toss with olive oil and roast at 400 degrees F until soft, 35 to 45 minutes. Remove the skin. Puree the squash with 3 tablespoons butter; season with salt. Warm a few tablespoons of maple syrup with a pinch of cayenne pepper; drizzle over the mash.

Peel and roughly chop 3 pounds rutabagas. Place in a pot and cover with equal parts milk and water (about 2 1/2 cups each); add a pinch of salt. Bring to a simmer and cook until soft, 20 to 25 minutes; drain. Puree with 1/2 cup heavy cream and 2 tablespoons butter. Cook a few sliced garlic cloves and some fresh rosemary in olive oil; drizzle over the mash.