Preheat the oven to 375 degrees F. Spray a baking sheet with nonstick cooking spray and keep nearby.
Heat the oil in a large nonstick skillet over medium-high heat. Add the mushrooms, onion, and salt. Cook, stirring occasionally, over medium heat, until the mushroom mixture is very tender, about 8 minutes. Remove from the heat. Stir in the turkey, cream cheese, and Cheddar until well blended.
Place 1 sheet of phyllo with the short side facing you on a work surface. (Cover remaining phyllo with plastic wrap to keep from drying out.) Spray the phyllo sheet with nonstick cooking spray. Then fold it in half lengthwise and spray again. Place 1 heaping tablespoon filling in the center of the bottom end of the phyllo. Fold in the sides, then roll up from the bottom to completely enclose the filling (it should look like an egg roll). Place the roll, seam side down, on the baking sheet. Repeat with remaining phyllo sheets, nonstick cooking spray, and filling to make a total of 16 rolls.
Spray the rolls generously with nonstick cooking spray and bake until the rolls until lightly golden, about 20 minutes.