For the caramelized onions: In a large saucepan over medium-high heat, melt the butter. Once melted and bubbling, add a large handful of the onions and cook until translucent, 1 to 2 minutes. Repeat until all the onions have been added. Season with a pinch of salt and black pepper. Reduce the heat to low and cook, stirring occasionally, until the onions turn medium brown, about 30 minutes. If the onions start to get too dark, add 1 to 2 tablespoons of beef stock as necessary. Add the sherry to deglaze the pan. Add the mustard and stir to coat. Season with salt and pepper. Remove from the heat and set aside.
For the potato gratin: Preheat the oven to 400 degrees F.
Using a mandoline or a sharp knife, cut the potatoes into thin slices. Do your best to keep the potatoes in a stack--this will make it easier to layer them in the pan. Set the potatoes aside.
Use the reserved butter wrapper to lightly grease the bottom and sides of a large (12-inch) cast-iron skillet. Discard the wrapper.
Arrange a thin shingled layer of potatoes in concentric circles around the skillet. Season the potatoes with salt and pepper, then arrange an even layer of caramelized onions on top of the potatoes. Season with salt and pepper.
In a medium bowl, combine the Gruyere and mozzarella and reserve half for later use. Sprinkle on a layer of the remaining cheese mixture over the onions. Repeat the layers until all the ingredients (not including the reserved cheese) have been used. Press down firmly on the layers to flatten.
In a large bowl or measuring cup, combine the heavy cream and beef stock and pour over the gratin. Cover the skillet with foil and place on a sheet pan. Bake the potatoes, covered, until the top and edges have begun to brown and the potatoes are tender, 1 hour 15 to 1 hour 30 minutes. You can test by inserting a knife into the potatoes; if it goes in and comes out without resistance, then the potatoes are done.
Remove the skillet from the oven, remove the foil and turn the broiler on high. Combine the croutons and French fried onions. Cover the gratin with a layer of the crouton mixture followed by the remaining cheese. Broil until golden brown and bubbly, 5 to 8 minutes. Serve and enjoy!