A cutting head for a food product cutting system includes a generally cylindrical rotatable body, having a radius and configured to rotate about an axis, and a plurality of spatially separated, generally parallel elongate cutting blades, arranged in a circular array centered on the axis and defining a perimeter of the body. Each blade has a long dimension and an outwardly-oriented cutting edge. The generally cylindrical rotatable body is connectable to a driving mechanism configured to rotate the cutting head about the axis, and is positionable adjacent to a food product delivery mechanism, whereby food product that contacts the cutting edges of the array of blades in a direction generally perpendicular to the axis is cut by the blades into slices having a repeatable curvature.