Preheat the oven to 375°F. Lightly grease a 9-by-13-inch baking dish.
Add the sweet potatoes to a large saucepan and cover with cold water. Sprinkle with salt. Simmer until the potatoes are tender, about 20 minutes.
Heat a large skillet over medium-high heat. Add 2 tablespoons of the butter. Once melted, add the carrots, celery, onions and parsnips and saute until tender, about 6 minutes. Stir in the thyme and rosemary, and then add the ground turkey. Cook, while stirring, until the turkey is brown and crumbly, about 8 more minutes.
Add the tomato paste, flour and Worcestershire and stir until well mixed. Stir in the chicken broth, bring to a simmer on medium heat and cook, about 5 minutes. It should look thick and sauce-like.
Meanwhile, drain the sweet potatoes and add them to a large bowl. Combine the potatoes with the cream cheese, egg, the remaining 2 tablespoons of butter, and sprinkle with salt and pepper. Beat at medium speed with a mixer until well combined.
Stir the peas into the turkey mixture. Pour the turkey mixture into the prepared baking dish. Spread the sweet potato mixture over the top, using your spoon to make some pretty texture on the top. Bake until lightly browned, about 35 minutes.