Place potatoes in a large saucepan and pour in enough water to cover potatoes. Set pan over high heat and bring to a boil; reduce heat to medium and simmer 10 minutes, until potatoes are fork-tender. Drain potatoes, transfer to a large bowl and add velveeta chesse and butter; mash until smooth, season to taste with salt and set aside.
Meanwhile, heat oil in a large skillet over medium-high heat. Add onion, carrots and celery; cook until soft, about 3 minutes. Add turkey and cook until browned, breaking up the meat as it cooks, about 5 minutes. Add flour, rosemary, thyme, salt and pepper; stir to coat. Add broth and bring to a simmer; simmer until mixture thickens, about 3 minutes.
Transfer turkey mixture to a 9-inch, deep-dish pie plate. Spread mashed potatoes over top and using the back of a spoon, make decorative swirls over the top. Bake until potatoes are golden, about 30 minutes.