Cook the chicken: Poach or bake the chicken breasts until they reach 165°F internally, about 20 minutes. Let cool slightly before shredding with two forks.
Sauté the onion: Heat olive oil in a skillet over medium heat and cook diced onion for 3 to 4 minutes until softened and translucent.
Mix the filling: In a large bowl, combine shredded chicken, sautéed onion, black beans, green chiles, Greek yogurt, cumin, and garlic powder. Stir until evenly coated.
Warm the tortillas: Heat each corn tortilla in a dry skillet for about 20 seconds per side so they become pliable and don't crack when rolled.
Prep the baking dish: Spread about 1/2 cup of enchilada sauce over the bottom of a 9x13-inch baking dish to keep the tortillas from sticking.
Fill the tortillas: Spoon roughly 1/3 cup of the chicken filling down the center of each tortilla.
Roll and arrange: Roll each tortilla snugly and place seam side down in the prepared baking dish, fitting them close together.
Add remaining sauce: Pour the rest of the enchilada sauce evenly over the rolled tortillas, making sure the edges are covered to prevent drying out.
Top with cheese: Sprinkle the shredded cheese blend evenly across the top of the dish.
Bake until bubbling: Bake at 375°F for 20 to 25 minutes, until the sauce bubbles at the edges and the cheese turns golden in spots.
Rest before serving: Let the dish sit for 5 minutes out of the oven so the filling sets and slices hold their shape.
Garnish and serve: Sprinkle chopped cilantro over the top before bringing the dish to the table.