How to Make It
In a saucepan, boil the potatoes in salted water until tender, about 25 minutes; drain. Rice or finely mash. Measure out 1 1/3 cups of potatoes.
Meanwhile, in a medium bowl, combine the yeast with the warm water and 1/2 cup of the flour. Cover tightly with plastic wrap and let stand for about 25 minutes, until the mixture is frothy.
In the bowl of a standing electric mixer fitted with the paddle, beat the yeast mixture with the mashed potatoes, 3 tablespoons of the olive oil, 2 teaspoons of salt and the remaining 3 cups of flour at medium speed for 2 minutes. Switch to a dough hook and knead until a soft, slightly sticky dough forms, 5 minutes. Transfer the dough to a lightly oiled bowl; turn to coat. Let stand, covered, in a warm, draft-free spot until doubled in bulk, about 1 hour.
In a skillet, cook the leeks with the thyme, salt and sugar in the olive oil over moderate heat, stirring, until caramelized, 15 minutes.
Lightly oil an 11-by-17-inch baking sheet. Transfer the dough to the baking sheet and press to form an 11-by-17-inch rectangle. Lightly brush the dough with olive oil; let stand, loosely covered, in a warm, draft-free spot until puffy, about 35 minutes.
Preheat the oven to 425°. Using your fingers, make indentations all over the dough surface. Top with the leeks, cheese, sea salt and 1 tablespoon of the truffle oil.
Bake the focaccia on the middle rack of the oven for 20 minutes, until the cheese is bubbling and the crust is golden brown. Transfer the focaccia to a rack and brush with the remaining 1 tablespoon of truffle oil. Let stand for 30 minutes to cool slightly. Slice into squares and serve.