1. Preheat oven to 350 degrees Fahrenheit.
2. Peel and slice potatoes into 1/4-inch rounds. Set aside.
3. In a medium saucepan, melt butter over low flame. Stir in the flour, then mayonnaise and broth. Raise heat until the sauce reaches a rolling boil, stir, and allow to simmer until thickened.
4. Spread 1/4 cup of sauce on the bottom of an eight-inch pan. Place one layer of potato slices, then sprinkle half of the cheese. Repeat layers. Pour one teaspoon of milk into each corner of the pan, cover tightly, and bake for an hour and a half.
5. Place crackers in a small bag and crush by hand for 30 seconds. Remove potatoes from oven, sprinkle crackers over, and bake uncovered for 10 minutes.