Spay a large, nonstick skillet with non-fat cooking spray and set over medium-high heat. Add in onions and garlic and sauté until tender, about 2-3 minutes. Add in ground turkey, and cook while breaking it up with a wooden spoon. Add in chicken broth while cooking to keep meat from sticking to the pan.
Add in grated sweet potato, cumin, parsley, paprika, cinnamon, allspice, salt, and pepper. Taste, and add additional seasonings if desired. Cook until turkey is browned. Remove from heat and set aside.
Remove phyllo sheets from the package, and start by laying out two sheets, on top of each other, on a large flat surface.
Add 1/3 of the cooked ground turkey to one end of the phyllo sheets, and roll up like a burrito. Repeat this method to make two more logs.
Line a baking sheet with parchment paper and spray with non-fat cooking spray. Place logs on a baking sheet, and brush tops with melted butter. Bake at 350 degrees for about 20 minutes until golden brown.