Roast the poblano chiles under the broiler until blistered on all sides. Transfer to a plastic bag, seal tightly and allow to steam for 15-30 minutes. Take the chiles out of the bag, remove the blistered skin (it should peel off easily) and cut peppers in half lengthwise. Remove ribs and seeds from peppers. Cut roasted pepper into 1-inch pieces. Put aside.
Heat 2 tablespoons of vegetable oil in a large Dutch oven over medium high heat. Season chicken pieces with salt, black pepper, and ½ teaspoon of ground cumin. Transfer half of the chicken pieces to the Dutch oven and sauté until golden brown, stirring from time to time, about 6 minutes. Transfer to a bowl, add one more tablespoon of oil to the skillet and sauté the rest of the chicken. When it is golden, transfer it to the bowl that the other cooked chicken is in.
Add one tablespoon of oil to the pan and put chopped onions in. Stir frequently, and cook until softened, about 6 minutes.
Add the jalapeno and garlic and stir for one minute. (If the fond on the bottom of the Dutch oven from cooking the chicken becomes very brown during this time, add 1/2 cup of the chicken broth and scrape the bottom of the pan to loosen the fond and flavor the aromatic base.)
Add the canned chiles and the chopped poblano chiles, the remaining 1 teaspoon of cumin and the oregano. Stir well, allowing the cumin and oregano to release their flavors, about 1 minute.
Return the chicken pieces and any juices that have collected to the pan. Add the chicken broth, stir well, and bring to a boil. Lower heat to simmer and cook uncovered for 20 minutes, stirring occasionally.
Add tomatillos to simmering mixture, cover and cook for 30 minutes.
Five minutes before serving, add zucchini quarter rounds to chile verde.
Serve in bowls with suggested condiments and warm tortillas.