-
1
Bring chicken, water, 2 onion quarters, and 1 teaspoon salt to a boil, covered, in a 4- to 5-quart pot over moderately high heat.
-
2
Boil 10 minutes, then remove from heat and let stand, covered, until chicken is just cooked through, about 10 minutes.
-
3
Transfer chicken to a plate, reserving broth with onion.
-
4
When cool enough to handle, coarsely shred chicken, discarding skin and bones.
-
5
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.
-
6
Peel garlic and transfer with onion to a blender.
-
7
Add tomatoes with juice, chiles, and oregano, then puree until smooth.
-
8
Cook chorizo in oil in a 12-inch heavy skillet over moderately high heat, stirring, until fat is rendered, about 2 minutes.
-
9
Carefully add puree (it will splatter and steam) and cook, stirring frequently, until thick, about 10 minutes.
-
10
Peel potatoes and cut into 3/4-inch pieces, then add to reserved broth with remaining teaspoon salt.
-
11
Simmer, covered, stirring occasionally, until potatoes are almost tender, about 10 minutes.
-
12
Add potatoes and onions to chorizo mixture along with 2 cups broth (save remainder for another use).
-
13
Stir in chicken and simmer 10 minutes.
-
14
Serve sprinkled with cheese.
-
15
*Available at Latino markets and some specialty foods shops.
