Season turkey legs on all sides with 1/4 tsp each of salt and pepper. In large Dutch oven, heat olive oil and sear turkey legs on medium-high heat, turning every 2 to 3 minutes to brown each side. Remove turkey legs to plate and set aside. Add onion and leek to Dutch oven and sauté on medium heat until soft, for 3 to 5 minutes.

Return turkey to Dutch oven, increase heat to high, and add thyme sprig and stock to cover. Bring to a boil, then reduce heat to medium-low and simmer gently, covered, for 1 1/2 to 2 hours, until meat begins to fall from turkey bone. Transfer turkey legs to plate using fork, remove skin, and separate meat from bone. Remove thyme sprig.

Return meat to Dutch oven. Discard bones and skin. Add carrots and parsnips and simmer, uncovered, on medium for about 30 to 40 minutes, until vegetables are tender.

Just before serving, add frozen peas, stir through, and simmer for 5 minutes to heat thoroughly. Taste and adjust seasoning, if required, with remaining salt and pepper. Serve stew in shallow dishes, sprinkled with tarragon and accompanied by crusty bread, or over rice.