Char the poblano pepper over an open flame or under the broiler until the skin is blistered and blackened.
Place the pepper in a bowl and cover with plastic wrap for 5 minutes, then peel off the skin, remove seeds, and dice the flesh.
Heat olive oil in a skillet over medium heat and sauté the onion and garlic until fragrant and translucent.
In a medium bowl, combine the shredded chicken, diced poblano, sautéed onions, cumin, salt, and pepper.
Whisk together the Greek yogurt and salsa verde in a small bowl to create the creamy green sauce.
Warm the corn tortillas slightly to prevent cracking, then fill each with the chicken mixture and roll tightly.
Place the tortillas seam-side down in a baking dish, top with the creamy sauce, and bake at 375°F for 15 minutes until bubbling.
Garnish with fresh cilantro and serve immediately.