Heat oven to 425°F. Toss squash with 1 tablespoon oil and 1/8 teaspoon salt on sheet pan. Roast 25 to 30 minutes, turning once, until tender with browned edges.
Heat remaining tablespoon oil in soup pot over medium. Cook onion 6 minutes, then garlic, cumin, chipotle, and adobo sauce 1 minute.
Add half the roasted squash and 2 cups broth; simmer 3 minutes. Remove from heat; carefully immersion-blend smooth.
Add remaining broth, hominy, ham, and reserved squash. Gently simmer 10 minutes until hominy hot and ham 165°F.
Off heat, stir in lime juice and cilantro. Taste; add remaining 1/8 teaspoon salt only if needed.
Divide among six bowls, distributing hominy, ham, and squash evenly.