Preheat oven to 400 degrees F. Heat a large skillet over medium heat. Add olive oil. Once hot, add ground turkey, onion, salt, cumin and green chiles with their juices. Break up with a wooden spoon and cook until no longer pink.
Spread 1/4 cup salsa verde in the bottom of a 13x9 baking dish. Set aside.
Line a plate with paper towels then set to the side. Heat a small skillet over medium heat. Add 1/4-inch of vegetable oil to the pan. Once oil is hot, add a corn tortilla and cook for 10 to 15 seconds per side. You want the tortillas to soften but not get crispy. Remove from the oil and place on the paper towel lined plate. Allow tortillas to cool slightly before handling.
Fill a tortilla with a few tablespoons of turkey filling. Roll the tortilla and place seam side down into the prepared baking dish. Repeat until you've used up all the tortillas and turkey. Sprinkle the enchiladas with the shredded monterey jack then drizzle with the remaining 3/4 cup salsa verde. Bake for 15 minutes.
Optional: top with sour cream and cilantro for serving.