Heat the olive oil in a large skillet over medium-high heat. Add the turkey and season with the garlic powder, onion powder, smoked paprika, salt, and pepper.
Cook for 6 to 8 minutes, breaking the turkey apart, until fully cooked and browned. Remove to a plate.
In the same skillet, add the onion and cook for 2 minutes. Add the peppers and garlic and cook for 1 minute more.
Pour in the stock and cover the skillet immediately. Reduce heat to medium-low and steam for 4 to 5 minutes, until the peppers are crisp-tender.
Uncover, return the turkey to the skillet, and stir to combine. Cook uncovered for 2 to 3 minutes, until excess liquid reduces.
Top with the cheese if using, cover briefly until melted.
Garnish with cilantro and serve with lime wedges.