2 1/4 cups finely diced, peeled eggplant
1 teaspoon coarse salt plus more to taste
1/4 cup plus 2 tablespoons safflower oil
3 tablespoons minced shallots
1/4 cup (1/2 stick) unsalted butter
Place eggplant in a nonreactive bowl. Toss with 1 teaspoon of salt and allow to sit for 20 minutes. Remove to a clean kitchen towel and tightly twist to squeeze out all moisture. Set aside. Heat 2 tablespoons of oil in a medium sauté pan over medium heat. Add the eggplant and shallots and sauté for about 6 minutes, or until very tender. Remove from heat and set aside. Peel potatoes. Using a hand grater or mandoline, shred potatoes into a clean kitchen towel. Tightly twist to squeeze out as much moisture as possible. Preheat oven to 375°F. Heat remaining 1/4 cup of oil in a 9-inch ovenproof, nonstick sauté pan over medium heat. Using a spatula, evenly press half of the potatoes into the pan. Season to taste with salt and pepper. Spread the reserved eggplant over the top. Pat remaining potatoes evenly over the eggplant. Again, season to taste with salt and pepper. Cook for about 10 minutes, or until bottom is golden. Carefully turn and dab the crust with bits of butter. Cook for about 5 minutes, or until bottom begins to crisp. Place in the preheated oven and bake for 25 minutes, or until potatoes are cooked and tart is golden and crisp. Remove from oven and allow to rest for 5 minutes. Using a sharp serrated knife, cut into 6 wedges and serve immediately.