Char the poblano pepper over a gas flame or under the broiler until the skin is blackened, then place in a bowl covered with plastic wrap for 10 minutes before peeling, seeding, and dicing.
Preheat your oven to 375°F and lightly grease a small baking dish.
In a mixing bowl, combine the shredded cooked chicken, diced poblano, diced yellow onion, cumin, garlic powder, sea salt, black pepper, lime juice, and 1 tablespoon of the Greek yogurt.
In a separate small bowl, whisk together the remaining Greek yogurt and the salsa verde until a smooth, creamy sauce forms.
Warm the corn tortillas in a dry skillet over medium heat for about 30 seconds per side until they are soft and pliable.
Place a portion of the chicken mixture into each tortilla, roll them up tightly, and arrange them seam-side down in the prepared baking dish.
Spread the creamy salsa verde sauce evenly over the top of the tortillas and sprinkle with the shredded Monterey Jack cheese.
Bake for 15 to 20 minutes until the cheese is melted and the edges of the tortillas are slightly crisp.
Garnish with fresh chopped cilantro and serve immediately.