Special equipment: a mandoline
Preheat the oven to 375 degrees F.
In a 10-by-10-by-2-inch casserole, arrange some of the potatoes in an even layer, drizzle with 3 tablespoons of the cream and season with salt and pepper. Repeat with the remaining potatoes, cream and salt and pepper to form 11 layers. Press down on the layers to totally submerge them in the cream.
Cover and bake for 30 minutes; remove the cover and continue baking until the cream has been absorbed, the potatoes are cooked through and the top is browned, 30 to 45 minutes longer. Evenly distribute the Caramelized Shallots and Fried Sage Leaves over the top.
Melt the butter in a large saute pan over medium heat. Add the shallots and sugar and slowly cook, stirring occasionally, until golden brown and caramelized, about 40 minutes; season with salt and pepper.
Heat the oil in a small saucepan over medium heat until it begins to simmer. Add the sage leaves in batches and fry for a few seconds until crisp. Remove with a slotted spoon to a plate lined with paper towels and season with salt.
Cover and refrigerate the flavored oil to save for sauteing fish, chicken or pork chops.