Prepare the toppping
Clean the sweet potatoes and stab with a fork or knife. Position on a paper towel in the microwave and microwave on high for 6-8 minutes, turning over once. Microwaves vary in strength. Continue baking the sweet potatoes for a few more minutes if necessary.
When cool enough to handle, scoop the flesh into a medium mixing bowl. Add the milk, cheese, butter, 1/4 tsp. salt, and 1/2 tsp. pepper and beat with a whisk or an electric hand mixer on low speed until smooth and creamy, about 1 minute. Set aside.
Prepare the filing
Heat the oil in a 12-inch sauté pan over medium-high heat. Add the celery, carrot, onion, and ¼ tsp. salt. Reduce the heat to medium and cook, stirring frequently, until the vegetables are soft, fragrant, and starting to turn golden, 10 to 15 minutes. Add the garlic, cumin, oregano, chile powder, and cinnamon and cook for 30 seconds. Add the turkey, season with 2 tsp. salt, and cook until no longer pink, about 5 minutes. Add the peas and cook for another minute; season to taste with salt.
Assemble and bake the pie
Transfer the beef mixture to a 9x9-inch baking dish. Spread the sweet potatoes over the top in an even layer. Bake until bubbling around edges, about 30 minutes.