Heat the oil in a medium ovenproof skillet over medium-high heat. Add the garlic, carrots and onions; cook until tender and beginning to brown, about 5 minutes.
Add the turkey and thyme, and continue to cook, breaking the turkey up with a spoon, until the turkey is cooked through and lightly browned.
Stir in the ketchup and cook until lightly caramelized.
Stir the broth and flour together in a small bowl until smooth, and then pour into the skillet.
Cook until thickened, about 2 minutes. Stir in the peas and season with ¼ teaspoon salt.