Thaw the frozen phyllo pastry sheets in the refrigerator overnight, and then bring these to room temperature prior to use for easier handling.
Drain the feta cheese from the brine. Cut the block of feta using a thin, sharp knife into 6 slices, approximately 2 by 4 inches and 1/2-inch thick. Set the slices on a clean kitchen towel to dry.
Lay the phyllo sheets on a flat surface and cut with kitchen scissors or a small sharp knife to size. They should be cut into rectangles, approximately 8 by 12 inches. Use a ruler if needed.
Lay 1 cut piece of phyllo in front of you like a sheet of wrapping paper - the 12-inch length top to bottom. Place a slice of feta at the top end of the sheet slightly below the edge and wrap it up as you would a small package. Fold the top end of the sheet over the feta and then fold the left and right sides over. Flip the partly wrapped feta down the sheet towards you until it is fully wrapped. If needed, a little water can be used to seal the last edge of the sheet onto itself.
Set aside with the sealed edge on the bottom of the package so the weight keeps the phyllo closed. Do not stack packages on top of each other. Continue to wrap all the pieces of feta.
Heat the oil to 350 degrees F in a deep sided skillet using sufficient oil to float the package, about 3 to 5 inches of oil. Fry to a golden brown, about 5 minutes on each side. The pastry should puff up slightly. Remove with tongs or a slotted spoon and drain on a paper-towel lined plate.
Serve each package on an individual plate or, if on a serving platter, do not stack the packages. Drizzle each package with about 2 tablespoons of honey and sprinkle with a teaspoon of black sesame seeds. Top with cut pieces of candied fig or a teaspoon of chunky fig jam.
Cook's Note: Uncooked packages can be frozen for later use. If freezing, dust lightly with cornstarch or flour to help keep them separate.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.