Preheat oven or your fancy backyard smoker to 350 degrees. Slice green tops off leeks and cut lengthwise. Soak in water to clean thoroughly, and then thinly slice. In a medium sauté pan over medium heat, melt butter and add leeks and salt and pepper to taste. Cook about 5 minutes, stirring occasionally to prevent browning. Take off heat and add artichokes and mustard. Mix thoroughly. Once cooled, stir in ¾ of the cheese.
Using food processor slicing disk or mandolin, thinly slice potatoes, then transfer to large bowl and add cold water to cover. Stir with hands to rinse then drain well. Layer potatoes between paper towels and pat dry.
Layer 1/3 of potatoes in bottom of a lightly buttered casserole dish, overlapping slightly. Salt and pepper. Evenly spoon 1/2 of leek-cheese mixture over top. Top with second layer of potatoes, salt and pepper, then remaining leek-cheese mixture, then final layer of potatoes. Slowly pour cream over top. Cream should come up about 3/4 to the top of the potato mixture. Top with remaining cheese. Cover casserole with foil, careful not to press to close to the cheese topping.
Cook covered for 40 minutes, until cheese melts. Uncover and continue to cook until potatoes are tender, and cheese is brown, about 20 more minutes. Serve warm.