A method is described for making a frozen French fry-style food product, having from about 50.0% to about 70.0% moisture, from about 4.0% to about 8.0% protein, from about 2.5% to about 5.0% fat, and from about 0.25% to about 0.50% fibers, in addition to calcium and phosphorous sources. This frozen potato-based product is made from a composition comprising steam peeled and cooked whole raw potatoes, soaked or cooked whole beans processed and mixed with the peeled cooked potatoes to create a dough-like consistency to which proteinaceous flours, starchy flours, vegetable oil, and other additives are added and blended into a homogeneous potato-based dough. The homogeneous potato-based dough is extruded into a rope-like extrudate, which is partially steam-cooked and then immediately cooled. The cold rope-like extrudate is cut into uniform small rods, 2.5 inches long, which are packaged and stored under blast freezing conditions.