Rinse potato batons in a large bowl with lots of cold running water until water becomes clear. Cover with water by 1 inch and add ice. Refrigerate at least 30 minutes and up to 1 day.

In an Emerilware/T-Fal fryer or other electric fryer, heat oil to 325 degrees. Be sure not to fill beyond the maximum fill line.

Drain water from potatoes and wrap in a clean dishcloth or tea towel and thoroughly pat dry. Add potatoes, a handful at a time, to hot oil and fry, stirring occasionally, until potatoes are soft and limp and begin to turn a blond color, 6 to 8 minutes. Carefully remove fries from oil and set aside to drain on paper towels for at least 10 minutes and up to 2 hours.

When ready to serve, reheat oil to 350 degrees. Transfer potatoes to hot oil and fry again, stirring frequently, until golden brown and puffed, 3 to 4 minutes. Transfer to paper towels to drain, and season with salt and pepper. To serve, spoon 1/3 cup Beef Gravy onto a large platter, top with fries, and top additional gravy if desired. Add Cheddar Bechamel over top. Serve immediately.