In a bowl, stir barbecue and buffalo sauce in with the cooked chicken, stirring to coat. Fold in the cheeses.
Melt 4 tablespoons butter and set aside. Prepare a large sheet pan with a layer of nonstick foil or parchment paper.
Take your fillo dough and lay out one sheet on a clean surface. Brush it with a little of the melted butter and sprinkle lightly with breadcrumbs (the breadcrumbs will create a bit of separation between each layer of fillo). Put another layer of fillo dough on top, and repeat the butter and breadcrumb process again and again until you have 4 layers.
Spoon half of the curry chicken mixture along one edge (lengthwise) of the fillo. Roll it up tightly and set the roll seam side down on the prepared baking sheet.
Repeat the process with the rest of the fillo and chicken mixture to make a second roll. Brush each roll with the rest of the melted butter and score both rolls diagonally into 1-inch pieces with a serrated knife. You want to cut them about ¾ of the way down, without cutting all the way through.
Bake for 20 minutes, or until the top is golden brown (*check the Free Tip section). Let rest for 10 minutes before slicing the rest of the way through. Serve warm or at room temperature and with ranch or blue cheese salad dressing for dipping.
You can add thinly sliced and sautéed red onions to the mix.
Substitute oil with butter.
Oven temperatures vary. Keep your eye on the fillo during the last 5 minutes of baking. Also, fillo thickness varies. Reduce the baking to 12-15 minutes if using extra thin fillo sheets.
Use jackfruit instead of chicken for a vegetarian version.