Preheat oven to 375 degrees F. Lavishly grease a cookie sheet or (preferably) cover it with parchment paper.
Melt 1 tablespoon of the butter in a large saucepan. Add the optional onion and cook for about 5 minutes, until it's translucent. Add the rice and chicken broth. Bring to a boil and cook for 15 minutes, or until the rice had absorbed all the broth. Cook to lukewarm, then season to taste with pepper and stir in the optional parsley.
Meanwhile, melt the rest of the butter in a small saucepan. Put 1 filo sheet in front of you and brush it lavishly with melted butter. Repeat this brushing process, using plenty of butter, stacking the sheets, until all the sheets have been used.
Carefully spread the cooled rice over the filo sheets, leaving a 2-inch border all around. Top the rice with the turkey and the turkey with the cheeses.
Slide your hand under a short end of the filo stack and lift up approximately 3 inches of it. Fold this over once, as if you were making the first fold in a business letter. Fold the long sides over to seal the filling. Continue folding until the strudel is all rolled up.
Place the strudel on the cookie sheet seam side down. With a sharp knife, make several slashes in the top to let out the steam. Bale for 35 to 40 minutes, or until the strudel is well browned and crisp-looking. (Some of the filling may leak out onto the pan, but don't worry about that.) Let the strudel stand for 5 minutes before you slice it with a sharp knife.