Heat a large skillet over medium-high heat. Add 1 Tablespoon canola oil, ½ teaspoon oregano, ½ teaspoon cumin, and ¼ teaspoon freshly ground black pepper. Cook until the spices start to sizzle and smell fragrant, about 30-60 seconds. Add the cubed chicken thighs and ½ teaspoon kosher salt. Cook, stirring often, until the chicken is browned, about 5 minutes. Transfer the chicken to a plate or bowl using a slotted spoon.
Add the remaining 1 Tablespoon canola oil to the skillet, then the minced onion and minced green bell pepper. Cook until the vegetables are soft, about 3 minutes. Stir in the minced garlic and cook until fragrant, about 1 minute.
Add the 2 4-ounce cans chopped green chiles, 1 cup chicken broth, and the browned chicken, plus any juices on the plate. Bring the mixture to a simmer, and reduce the heat to medium. Simmer until most of the liquid has cooked down, about 8-10 minutes.
While the chicken is simmering, heat the tortillas. You can do this on the grill, a dry skillet over medium-high heat, a toaster oven, or the microwave. Once heated, stack the hot tortillas together and wrap them in a clean dish towel to keep them warm and soft.
Place a scoop of chicken on each tortilla and serve as desired with shredded cabbage, sliced avocado, chopped tomato, cilantro, minced onion, and/or lime wedges.
Store any leftover chicken in an airtight container in the fridge for up to 2 days. Reheat the chicken in the microwave or in a skillet and serve with freshly heated tortillas.