To make the dip, whisk the mayonnaise and mustard together in a small bowl.
Heat the oil in deep-fryer or heavy-bottomed pot to 350 degrees F.
Add the potato sticks into a bowl of water and allow it to sit for 4 hours. Remove them from the water to paper towels to drain. Fry in batches, letting them cook until a pale gold color develops, about 2 minutes. Drain the fries on a paper towel-lined plate. Cooks Note: Soaking the potatoes in water for 4 hours is just a suggestion. You can skip this pre-step and go straight to frying.
Raise the temperature of the oil to 375 degrees F and fry the potatoes in batches until they just start to become golden, about 2 minutes. Pull the potatoes out of the oil and let them stand for 1 minute. Drop the potatoes back into the oil and fry them until deep golden brown, about another 2 minutes. Drain the fries on a paper towel lined plate, and toss with salt and pepper, to taste. Transfer them to a serving bowl and serve hot with the mayonnaise dip.