dried wild mushrooms • olive oil • unsalted butter, plus more for greasing the pan • mixed fresh mushrooms, such as cremini or shiitake, trimmed and sliced ¼-inch thick • large (or 12 medium) fresh sage leaves, thinly sliced, plus more for garnish, if desired • small shallots, halved and thinly sliced • cognac (optional) • kosher salt, plus more to taste • Black pepper • medium leeks (340 grams or 12 oz), white and pale green parts only, halved lengthwise, thinly sliced and well washed • large eggs • heavy cream •