Place the potatoes into a large pot and cover with water. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until tender, about 20 minutes.
Drain, and allow to cool until the potatoes are cool enough to handle. Slice into 1/4-inch slices, and place into a 1-quart baking dish; set aside.
Preheat an oven to 350 degrees F (175 degrees C). Stir the cracker crumbs and melted butter together in a small bowl; set aside.
While the potatoes are cooking, melt 2 tablespoons of butter in a saucepan over medium-low heat.
Whisk in the flour, and stir until the mixture becomes paste-like and light golden brown, about 5 minutes. Gradually whisk the milk into the flour mixture, and bring to a simmer over medium heat. Cook and stir until the mixture is thick and smooth, 10 to 15 minutes. Stir in the mustard, salt, pepper, and Cheddar cheese until the cheese has melted and the sauce is smooth; pour over the potatoes.
Sprinkle with the cracker crumbs.
Bake in the preheated oven until the crackers are golden and the sauce is bubbly, 35 to 45 minutes.
