Place the dried mushrooms in a medium-sized bowl. Pour the boiling water over top and let sit for 30 minutes. Drain the mushrooms and reserve the steeping liquid.
Heat the olive oil over medium heat until shimmering. Add the shallots and half the salt. Saute until slightly softened. About 2-3 minutes.
Add the mushrooms to the shallots and saute until softened and slightly caramelized. Deglaze the pan with the sake and add the remaining salt.
Pour the beef stock into the skillet and bring the mixture to a boil. Reduce the heat to a simmer and let cook for 15 minutes.
Place the cornstarch in a small bowl. Spoon off a small amount of the liquid from the skillet and add it to the cornstarch. Whisk to combine.
Pour the cornstarch mixture into the skillet and cook until thick enough to coat the back of a spoon.
Remove the gravy from the heat and keep warm until ready to serve.