Preheat smoker or oven to 375℉.
Add the whole poblano and jalapeno peppers to a medium bowl with ½ tablespoon oil. Toss so that the peppers are coated in a thin layer of oil. Place directly on the grill grates, and allow the peppers to char and blister, turning every few minutes with tongs so that the peppers roast evenly. *If you don't have a smoker, a broiler or gas stove will work instead.
When the pepper skins are blistered all around, use tongs to remove the peppers from the grill and immediately place in a large bowl. Cover with plastic wrap and allow the peppers to steam in the bowl for about 10-15 minutes. Then gently peel off the pepper skin with your fingers, and dice the roasted peppers, removing the seeds and stems.
While the peppers are steaming in the bowl, make the green enchilada sauce. In a separate bowl, mix together canned diced green chiles, green enchilada sauce, and salsa verde. Stir well to combine. Set aside.
Make the enchilada filling. In a separate bowl, add the diced turkey, diced roasted peppers, sour cream, cream cheese, mayo, diced onion, cilantro, and about ½ of the shredded cheeses. Add 1 cup of the prepared green enchilada sauce from the previous step. Reserve the remaining enchilada sauce and shredded cheeses for the top of the enchiladas. Mix the filling well.
Prepare a 9″ x 13″ casserole dish by lining it with a thin layer of the prepared green enchilada sauce. Then warm the tortillas slightly to make them pliable. Fill each tortilla with a generous amount of the turkey filling (about 3/4 to 1 cup), roll them up, and place them seam-side down in the dish. *You should be able to fit 10 enchiladas in the dish.
Pour the remaining sauce over the rolled tortillas, and top generously with the rest of the grated cheese mix.
Place the dish in the preheated smoker or oven. Bake at 375°F until the cheese is bubbly and golden brown, approximately 30 to 40 minutes.
Carefully remove the enchiladas from the smoker or oven, and allow to cool slightly. Garnish with some more chopped fresh cilantro or sliced green onions. Serve with sour cream, hot sauce, or your favorite enchilada toppings.