In a large soup pot, heat 1 tablespoon oil over medium-high heat. Add the turkey and sauté for 2 to 3 minutes until the chicken is browned.
Remove the turkey from the pot and set it aside onto a plate.
Add the remaining tablespoon oil over medium-high heat and add the onions, carrots, and celery. Cook for 3 minutes or until the veggies are softened and golden brown. Add the seasonings, salt, pepper, potatoes, chicken broth, and turkey pieces. Bring to a boil, reduce heat, and simmer for 20 to 30 minutes, until the potatoes are fork-tender.
Stir in the green peas and half and half, cook for another 10 minutes, or until thickened. Remove the bay leaves and serve.