3 ½ - 4 pounds Idaho® russet potatoes, preferably long and slender (the amount of potatoes needed will depend on the size of your pan)
3 ½ - 4 pounds sweet potatoes (5-6 medium), preferably long, slender, and similar in shape and size to the russets.
4 tablespoons sweet butter (½ stick)
½ cup balsamic vinegar
1 cup plus 2 tablespoons apple cider syrup (or substitute pomegranate molasses)
20 fresh sage leaves, 5 finely chopped, 15 left whole
3 tablespoons extra virgin olive oil, divided
4 teaspoons kosher salt plus more, to taste
½ teaspoon freshly ground black pepper
Preheat the oven to 375ºF. Arrange oven rack in the center of the oven.
Grease the bottom and sides of a large (4 quart or larger), preferably round, casserole-dish, with butter or oil. Sprinkle 1 teaspoon of salt evenly over the bottom of the casserole.
Make brown butter: heat the butter in a medium saucepan (preferably light colored so you can see when it browns) over medium low heat. When it starts to foam, watch it carefully, whisking from time to time. It will slowly start to darken. When it turns from golden brown to dark brown and has a nutty aroma, remove it from the heat.
In a medium bowl whisk the cider syrup, balsamic vinegar, 2 tablespoons oil, chopped sage, 2 teaspoons salt and ½ teaspoon pepper. Pour the mixture into the pot with the brown butter and set aside.
Peel and cut the russet potatoes and sweet potatoes, crosswise, into very thin rounds, about 1/8 inch. I recommend using a mandolin or your food processor with the slicing blade attached. Transfer potato slices to the bowl with water and vinegar, as you cut them, to prevent discoloration.
Place a dishtowel on your work surface. Pull a handful of russets slices and a handful of sweet potato slices out of the water and lay them on the towel. Blot them dry with a second towel. Arrange a stack of alternating sweet and white potatoes in your hand. Set the stack on its side in your casserole like a long caterpillar. Lean a cup or bowl against the potato slices to keep them vertical, as you work. Repeat with remaining potato slices, winding the caterpillar around the perimeter of the casserole. Continue by creating an inner circle and then an even smaller one, if there’s room, until you've either filled your entire casserole or run out of potato slices. Adjust the rows of potatoes depending on how large your casserole is. If it's very tight, the slices will be straight up and down. For a very large casserole you can tilt the slices and spread them out more. (Note: you will probably have extra potato slices that will go unused)
Heat the cider-butter mixture until it starts to simmer. Give it a whisk, and pour it evenly over the potatoes.
Rub the sage leaves with a little olive oil to moisten them, and then arrange them, decoratively, on top of the tian, pressing them down against the potatoes, so they stick and are less likely to curl.
Sprinkle 1 teaspoon of salt and a few grinds of pepper over the tian. Cover the casserole tightly with foil and bake in the oven for 30 minutes.
Remove the foil. Cook the tian, uncovered, for 40-60 minutes longer, until the potatoes are cooked through and starting to brown on the edges. Cooking time will depend on the size of your casserole and how tightly packed the potatoes are.