heat oil in a large skillet over medium high heat. Add turkey and cook, breaking up with the back of your spoon until fully cooked. Add onion, garlic, and poblano pepper; cook another 3-4 minutes or so, until onion is translucent, pepper soft, and garlic fragrant. Season with salt and pepper.
Add in diced tomatoes, orzo, tomato paste, broth, and spices; stir to combine. Bring to a boil, reduce heat and simmer for 10-12 minutes, stirring frequently, until orzo is cooked and liquid has reduced.