Prepare the Potatoes: In a medium pot, bring salted water to a boil. Add the quartered new potatoes and cook until tender, about 15-20 minutes. Drain and let cool slightly.
Mash the Potatoes: In a bowl, mash the cooked new potatoes with a fork until slightly chunky. Stir in a pinch of salt and pepper to taste.
Assemble the Sub: Slice the sub rolls lengthwise without cutting completely through. Spread a layer of mayonnaise on one side and Dijon mustard on the other. Add a generous scoop of the mashed potatoes into each sub.
Toast the Subs (Optional): Preheat your oven to 375. Place the assembled subs on a baking sheet and toast in the oven for about 5-10 minutes, or until the bread is crispy and the cheese is melted.
Serve: Remove from the oven and allow to cool slightly. Cut in half if desired, and serve warm.
Notes
Optional toppings include sliced tomatoes and pickles.