Preheat oven to 375 degrees. Cook potatoes by placing them in a pot of cold, heavily-salted water and bringing to a boil. Reduce heat to simmer potatoes until cooked through (if water remains at a boil, potatoes will begin to break down and become soggy). Drain potatoes and, when cool enough to handle, slice lengthwise.
Add slab bacon to a cold pan and render over medium-low heat. (Starting in a cold pan maximizes rendering). Once crispy, remove bacon and drain on a paper towel-lined plate.
In same saucepan over medium heat, melt butter. Add flour, and cook, whisking constantly, for about 3 minutes. While continuing to whisk, add milk and bring to boil. Reduce heat and add half of gruyère to sauce and stir. Season with salt, pepper, and nutmeg.
In a shallow baking dish or ovenproof skillet, gently combine potatoes, bacon, chives, and cheese sauce, then top with remaining gruyère. Bake for 30 minutes, or until cheese begins to brown. Remove casserole from oven and crack eggs over it. Return to oven and bake until eggs have reached desired doneness (about 10 minutes for the whites to set)