Arrange racks in the upper and lower thirds of the oven; preheat to 400°F.

Wrap beets in foil, place them in a baking dish, and roast them on top rack, checking for doneness after 1 hour. Continue cooking until tender enough to pierce easily with a paring knife. Let cool until comfortable enough to handle, then peel by rubbing outsides with a paper towel or clean dish towel. Cut into 3/4-inch pieces.

Meanwhile, cut delicata in half lengthwise; scoop out seeds and pulp. Cut lengthwise again, and then slice into 1/4-inch quarter moons. In a medium bowl, combine 1 tablespoon oil, 1 tablespoon maple syrup, 1/2 teaspoon salt, and 1/4 teaspoon pepper; add delicata and toss until coated. Spread out in a single layer onto a baking sheet. Roast on lower rack, stirring once or twice, until tender and caramelized, 16–20 minutes. Remove from oven and set aside.

Reduce oven temperature to 325°F.

In a large bowl, toss bread, 3 tablespoons oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Spread on a parchment-lined baking sheet. Place on top rack and bake, turning cubes halfway through, until golden brown and crisp, about 25 minutes. Let cool slightly.

Meanwhile, in a small bowl, whisk grapefruit juice, garlic, thyme, mustard, 3/4 teaspoon salt, and 2 tablespoons maple syrup until well blended. Slowly whisk in 6 tablespoons of oil until the dressing is smooth.

Toss squash, beets, toasted bread, parsley, and pomegranate seeds in a large bowl. Slowly drizzle the dressing over the salad and toss again.

Transfer the bread salad to a platter. Top with goat cheese and grapefruit segments.