Step 1If the dough sheets are frozen, thaw them in the refrigerator 8 hours or overnight, or according to package instructions. Set the dough sheets aside to come to room temperature in their package; this takes about 2 hours.
Step 2To make the filling, mash and crumble the feta cheese with a fork in a bowl until it is finely crumbled. Add the dill and pepper and mix well.
Step 3Prepare a small bowl of water to moisten the dough. Unroll the dough sheets onto a cutting board. With a sharp knife, cut the stack of dough sheets in half crosswise, to get sheets that are about 8 inches wide. Immediately cover the sheets with plastic wrap, then with a slightly damp towel. Work with only 1 piece at a time, keeping the remaining sheets covered so they do not dry out.
Step 4To make a cigar, remove one piece of borek from the pile to a work surface, the shorter side of the rectangle facing you (“vertical” orientation). Spoon 1 tablespoon filling in a thin strip about 1 inch from the bottom edge, leaving about 1 inch clear on each end. Fold the bottom edge of dough over the filling, press so the filling is fairly tightly enclosed, and roll the dough over the filling again. Fold the two long sides of the filo, to your left and right, inward slightly over the filling, and press gently on these folds. Roll the pastry up fairly tightly in a finger shape. Before you finish rolling, dip your finger in water and moisten the end to stick the dough together. Press to adhere.
Step 5Set the pastry cigar on a plate. Cover with plastic wrap. Shape more cigars with the remaining dough and filling.
Step 6Heat a thin film of oil in a deep skillet. It should be hot enough so it sizzles when you dip the end of a pastry cigar in it. Fry 4 or 5 cigars at time over medium heat until golden, about 1 minute on each side. Remove to paper towels. Serve hot or warm.