For the Mille-Feuille
If you have a chamber vacuum sealer, put an eighth sheet pan in a 12 by 15-inch (30 by 40-centimeter) sous vide bag, place in the sealer chamber, and vacuum seal. If you do not have a chamber vacuum sealer, spray an eighth sheet pan with nonstick spray. Line the pan with two layers of plastic wrap, extending it over the sides.
Put the clarified butter in a wide 3-quart (3-liter) saucepot, heat just enough to melt the butter, and keep warm.
Set a Japanese mandoline over a bowl. Slice the potatoes lengthwise into 1-millimeter-thick (paper-thin) slices. Adjust the blade as necessary to be certain that the slices are solid and of even thickness. Season with the salt. Gently toss the potato slices in the pan with the clarified butter to coat.
Overlap (shingle) the potato slices, alternating between the sweet potatoes and the russet potatoes (use 2 slices of sweet potato, then 1 slice of russet), in even rows to cover the bottom of the prepared sheet pan in a solid layer. Cover the potatoes with a piece of parchment paper, set a second eighth sheet pan on top, and press down to secure the potato slices in place.
Remove the top pan and the parchment and arrange a second layer of potato slices over the first. Continue to layer the potatoes, pressing with the parchment and sheet pan after each layer is complete. The final layer of potatoes should be level with the rim of the pan.
If you have a chamber vacuum sealer, set an immersion circulator in a water bath and heat the water to 88°C (190.4°F). Wrap the entire sheet pan twice in plastic wrap, place it in a 12 by 15-inch (30 by 40-centimeter) sous vide bag, and vacuum seal. Cook in the water bath for 1½ hours. Remove from the water bath and let rest for 15 minutes, then submerge in an ice-water bath until cold. Refrigerate for up to 2 days.
If you do not have a chamber vacuum sealer, preheat the oven to 300°F (150°C). Place a piece of parchment on top of the mille-feuille and seal the pan with a piece of aluminum foil. Bake for about 1 hour, until a cake tester inserted into the potatoes meets no resistance. Remove the foil but leave the parchment over the top. Set a second eighth sheet pan on the parchment and add weight to the pan to compress the potatoes; let stand for about 30 minutes. Transfer the potatoes with the weights to the refrigerator and refrigerate for at least 6 hours or up to 2 days.