In a large skillet, warm oil over medium heat. Stir in onion, cover and cook, stirring occasionally, until just beginning to color, 5 to 6 minutes. Stir in cumin and oregano.
Add turkey; raise heat to medium-high. Cook, stirring often, until cooked through and most of liquid evaporates, 12 to 15 minutes. Stir in chiles, tomatoes, salt and pepper. Cook until some of liquid has evaporated, about 10 minutes. Garnish with oregano leaves.