Char poblanos and jalapeño in a 450° oven. I do this by putting the poblanos right on the grate with a sheet pan below it and turn occasionally until evenly charred. If I’m doing the smaller peppers I’ll put them on aluminum foil so they don’t fall through. The little ones won’t take as long to char, so just check as they are cooking. Peel and deseed poblanos, trim jalapeños, and add all to a food processor. Blend until smooth, adding a little water if necessary.
Meanwhile, rinse and peel the shrimp, reserving shells. In a saucepan, boil shrimp shells with 3 cups water for half an hour to create a shrimpy broth. Drain and reserve the broth, adding enough water to get it back up to three cups.
In a soup pot, heat oil on medium and cook onion until translucent and beginning to turn golden. Add garlic and stir for a minute or two, then cumin, coriander, and salt and stir until fragrant. Add the shrimp broth, the pepper mixture, and the hominy and simmer for 20-30 minutes, stirring occasionally, and adding more water if necessary to keep a somewhat thick somewhat brothy consistency. Stir in shrimp and cook until they just turn pink. Stir in spinach and oregano and cook for another few minutes. Taste and adjust seasoning if necessary.