Preheat oven to 375 degrees F. Grease a 9-inch x 13-inch baking dish and set aside.
Put sweet potatoes into a large pot and cover with water. Place over medium-high heat and bring to a boil. Cook until fork tender, about 20 minutes.
While the sweet potatoes cook, heat a large skillet over medium-high heat and add olive oil. Once the oil is hot, add carrots, celery, and onion. Cook until soft and onions are translucent, about 5 to 7 minutes.
Add salt, pepper, thyme, rosemary, and ground turkey. Cook until turkey is browned, being sure to break up turkey as it cooks.
Add the tomato paste, flour, Worcestershire sauce, and chicken broth to the skillet. Stir to combine and bring to a simmer.
Drain the sweet potatoes and return to the pot - keep off the heat. Smash until smooth with a potato masher. Once smooth, add in butter, cream cheese, salt, and pepper. Stir until cream cheese is melted and combined.
Beat egg in a small dish. Add a couple of tablespoons of the sweet potato mixture to the egg and mix to temper. Add egg mixture into the pot of sweet potatoes and mix for a couple of minutes.
Add frozen peas to the ground turkey mixture in the skillet and stir. Pour turkey mixture into your prepared pan. Cover turkey and vegetables with the sweet potatoes, spreading them into an even layer.
Bake for 35 minutes until casserole is bubbling and potato crust is set. Remove from oven and let rest 5 to 10 minutes. Serve warm sprinkled with extra chopped thyme, if desired.