Soak the hominy and beans in separate bowls covered with 2 inches of water overnight at room temperature to soften them.

Drain the soaked ingredients and place them in a large pot, covering with 1 inch of fresh water. Bring to a boil, then reduce to a gentle simmer for about 1.5 hours, adding more water as needed so the ingredients stay submerged.

Check for doneness by splitting a bean and a kernel of hominy; they are ready when they are no longer chalky in the center. Stir in the salt and greens, simmering for another 10 minutes until the soup is thick and fully integrated.

Prepare the sauce by broiling tomatoes until the skins blister and char, about 8 minutes. Chop them coarsely once they are slightly cooled.

In a mortar and pestle, mash the ginger, garlic, and chile into a coarse paste. Incorporate the salt, cilantro, and roasted tomatoes until a chunky, assertive salsa forms.

Ladle the thick porridge into bowls and serve with a generous dollop of the pounded sauce to stir in as you eat.