For Vegetarian Posole, omit the chicken and add two 15-ounce cans pinto beans, drained. Reduce the simmering time to 30 minutes. To make with pork, omit the chicken and potatoes and brown 2 pounds cubed pork shoulder as for Red Posole before adding the onions. Proceed as directed, simmering until the pork is tender, 1 ½ to 2 hours.
Have ready:
Place in a blender and blend until smooth:
Heat in a large heavy soup pot over medium heat:
Add and cook, stirring occasionally, until tender, 6 to 8 minutes:
Add and stir until fragrant, about 30 seconds:
Increase the heat to medium-high and pour in the tomatillo mixture. Cook, stirring, until the mixture is at a brisk simmer and has turned olive green, about 5 minutes. Add the hominy along with:
Bring to a boil. Cover, reduce the heat, and simmer until the chicken is cooked through and the potatoes are tender, about 40 minutes. Remove the chicken from the pot and let sit until cool enough to handle. Shred the meat, discarding the bones or reserving them for stock. Return the chicken to the pot and season to taste with:
Simmer, uncovered, for 10 minutes. Taste and adjust the seasonings. Serve the posole, passing separately: