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While chicken is cooking, heat a dry well-seasoned small cast iron skillet over moderate heat until hot, then brown garlic and remaining 2 onion quarters on all sides, turning with tongs, about 5 minutes. Peel garlic and transfer with onion to a blender. Add tomatoes with juice, chiles, and oregano, then puree until smooth.
Cook chorizo in oil in a 12-inch heavy skillet over moderately high heat, stirring, until fat is rendered, about 2 minutes. Carefully add puree (it will splatter and steam) and cook, stirring frequently, until thick, about 10 minutes.
Peel potatoes and cut into 3/4-inch pieces, then add to reserved broth with remaining teaspoon salt. Simmer, covered, stirring occasionally, until potatoes are almost tender, about 10 minutes.
Garnish with avocado slices and warm corn tortillas, if desired.