Heat the oil in a medium pot over medium-high heat. Add the tomato paste and cook, smearing and stirring constantly with a heat-proof spatula or flat-edged wooden spoon, until dark and aromatic, about 90 seconds. Add the chipotle, chilli powder and oregano, and cook, stirring, for 1 minute. Stir in the salsa and 1 1/4 cup water. Stir in the beans and hominy. Bring to a boil, reduce the heat to medium-low, cover and simmer for 25 minutes, stirring occasionally.
Meanwhile, bring 1 1/2 cups water to a boil in a small saucepan with a lid. Stir in the rice, reduce the heat to medium low, cover and simmer until the water is absorbed, about 15 minutes. Remove from the heat and let stand, covered, 5 minutes.
Remove the chili from the heat, stir in the cider vinegar and let stand 1 minute. Fluff the rice with a fork, divide it among 6 serving bowls and top with the chili. Serve with pickled jalapenos and tortilla chips, if desired.
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