Place the potato wedges in a large bowl and cover with ice water. Let stand for at least 30 minutes and up to an hour. Drain the potatoes well. In batches, dry the potatoes on kitchen towels and let them sit for 30 minutes more to absorb any remaining moisture.
Fill a fryer or a large, heavy saucepan with 5 inches of oil. Place over high heat and bring the oil up to 315 degrees F. Set a wire rack on a sheet pan and place near the fryer or stove.
In batches to avoid crowding, add the potato wedges and fry, shaking them in the basket to separate them, or if in a large pot, stirring occasionally with a wooden spoon. Cook until the potato wedges are pale gold and slightly floppy, about 4 minutes. They should not be browned at this point. Remove from the oil with a wire skimmer and transfer to the wire rack to drain. Bring the oil back up to 315 degrees F and repeat with the remaining potato wedges. Remove the saucepan from the heat and set aside?do not throw out the oil. Let the potato wedges stand until completely cooled, at least 2 hours and up to 4 hours.
Meanwhile, prepare the gravy. In a high-sided skillet or medium saucepan, melt 2 tablespoons butter over medium heat. Add the shallots and cook until translucent, 4 to 5 minutes. Add the garlic and cook for 1 to 2 more minutes. Season with salt and pepper, then add the remaining 2 tablespoons butter and melt. Sprinkle the flour in the pan and cook, whisking until light brown, about 2 minutes. Whisk in the chicken stock and Worcestershire sauce. Continue whisking until there are no lumps. Let the gravy come to a bubble and cook until thick enough to coat the back of a spoon, about 5 minutes. Lower the heat and hold there, whisking regularly to keep it from sticking. Now it's time to finish the French fries.
Reheat the fry oil over high heat to 350 degrees F. In batches to avoid overcrowding, add the potato wedges to the hot oil and deep-fry until crisp and golden brown, 2 to 3 minutes. Transfer to a sheet pan and keep warm in a 200 degree F oven, if needed, while you fry the remaining potato wedges. Season with salt.
Preheat the broiler.
Arrange the potato wedges on a baking sheet or oven-proof platter. Pour the gravy over the top of the potato wedges and top with the shredded mozzarella. Place the baking sheet under the broiler until the cheese has melted, about 1 minute.
This recipe has been updated and may differ from what was originally published or broadcast.