Heat a large sauté pan over medium heat, and add 4 tablespoons olive oil. Add mushrooms and salt, and sauté 5 minutes, until mushrooms soften. Stir in garlic, lemon zest, lemon juice and tamari. Cook 1 more minute. Set pan aside.
If using raw dough, roll out thinly and place on a baking sheet. Prebake 10 minutes before adding toppings.
Brush pizza crust with remaining 1 tablespoon olive oil. Top with mushrooms and Parmesan. Bake 10 minutes, until crust is golden and cooked through.
Meanwhile, heat a medium sauté pan over medium heat. Add walnuts, and toast 3–4 minutes, until lightly browned and fragrant, stirring continuously. Roughly chop.
Garnish pizza with toasted walnuts and parsley, and drizzle with a touch of honey.
Tip: No need to remove shiitake stems; the cooking process will soften the stems sufficiently and maximize this flavorful mushroom.