To make the enchiladas: Heat the oil in a large skillet or sauté pan on medium heat. Once oil the is warm, add the peppers and onion. Cook, stirring occasionally, until the vegetables soften and the onions become translucent, about 8 to 10 minutes.
To the skillet, add the shredded chicken, 1/2 teaspoon salt, chili powder, garlic powder, cumin, and black pepper. Stir to coat evenly, then remove the skillet from the heat and let cool.
In a large bowl, combine 1 cup of the cheese, Greek yogurt, green chilies, and remaining 1 teaspoon salt. Once the chicken and veggie mixture has cooled to nearly room temperature, add it to the bowl with the yogurt mixture and stir to coat evenly.
To assemble the enchiladas: Fill each tortilla with a slightly heaping 1/2 cup of the chicken-yogurt mixture. Roll closed and place in the prepared dish, seam side down. Repeat with the remaining tortillas. Pour the green enchilada sauce evenly over the top, cover the pan, then bake for 30 minutes. Remove the pan from the oven, uncover, and sprinkle with the remaining 1 cup of shredded cheese. Bake uncovered for 5 additional minutes, until the cheese is melted. Sprinkle with desired toppings and enjoy!