Heat the olive oil in a large pot over medium heat. Add the turkey pieces and cook until lightly browned on all sides, about 5 minutes.
Add the onion, carrots, and parsnips. Cook for another 5 minutes, stirring now and then, until the onion softens.
Stir in the potatoes, barley, garlic, thyme, bay leaf, salt, and pepper.
Pour in the chicken broth and bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 35 to 40 minutes until the barley is tender and the vegetables are cooked through.
Remove the bay leaf before serving.