Set the pork in the freezer for 15 minutes. Drain the mushrooms, press out the water, and thinly slice.
Slice the pork into slices 1/4-inch thick. Stack the slices on top of each other and slice into 1/4-inch-wide strips. Place in a mixing bowl and add the cornstarch, sherry, soy sauce, white pepper, and 1 tablespoon of the peanut oil. Toss to coat.
Heat a large skillet over high heat until very hot. Add 1 1/2 tablespoons of the peanut oil and heat it until it begins to smoke. Add the pork, and stir-fry about 30 seconds, until almost cooked through, then transfer to a plate. Add the last 1 1/2 tablespoons of peanut oil to the skillet with 1 teaspoon of salt. Stir in the shiitakes and half of the sliced cabbage. Stir-fry over high heat until it starts to wilt. Add the rest of the cabbage and cook, stirring frequently, 1 1/2 minutes more. Return the pork to the pan and cook a minute or two, until heated through. Serve hot, with rice.