Heat oven to 425°F. Toss squash with 1 tablespoon oil and 1/8 teaspoon salt on a sheet pan and roast for 25 to 30 minutes, turning once, until tender and browned at the edges.
Heat the remaining tablespoon oil in a soup pot over medium heat. Cook onion for 6 minutes, then add garlic, cumin, chipotle and adobo sauce for 1 minute.
Add half the roasted squash and 2 cups broth. Bring to a simmer for 3 minutes, then remove from heat and blend carefully with an immersion blender until smooth.
Add the remaining broth, hominy, ham and reserved squash cubes. Simmer gently for 10 minutes until the hominy is hot and the ham reaches 165°F.
Remove from heat and stir in lime juice and cilantro. Taste and add the remaining 1/8 teaspoon salt only if needed.
Divide among six bowls with hominy, ham and squash cubes in every portion.