Heat oil over medium-high heat in a large heavy-bottomed pot. Add squash, onion, and 3/4 tsp. salt. Cook, stirring occasionally, until vegetables begin to soften, 7 to 8 minutes. Add tomato paste, garlic, chili seasoning, cumin, and oregano and cook 1 minute, stirring often. Add broth and hominy and bring to a simmer. Simmer, uncovered, until squash is tender, 12 to 15 minutes. Season to taste with salt.
Spoon into bowls and serve with cabbage, lime, avocado, radishes, and a basket of warm tortillas.
Wine pairing: La Crema 2014 Chardonnay (Sonoma Coast; $23)