Prepare the "fish" sauce. Add the shiitake mushrooms, miso paste, garlic, black peppercorns, tamari, and water into a medium saucepan, and bring to a boil. Reduce the heat to low and simmer, uncovered, until the sauce is reduced, about 30 minutes.
Prepare the pad thai sauce. Transfer 6 Tbsp./90 ml of the "fish" sauce into a small jar. Add the lime juice, maple syrup, and crushed red pepper flakes, and stir to combine. Set aside until ready to use.
Sauté the tofu. Crumble the tofu into a medium mixing bowl. Add the turmeric, season with salt, and stir until well combined. Heat the peanut oil in a large sauté pan over medium-high heat. Add the tofu and sauté until slightly browned, 5-7 minutes.
Sauté the vegetables. Add the cabbage, red pepper, and half of the pad Thai sauce into the pan with the tofu, and sauté until the cabbage begins to soften, 2-3 minutes. Next, add the carrot ribbons and sauté until the carrots begin to soften, 2-3 minutes. Finally, add the bean sprouts, green onions (reserve one green onion for garnish), and the other half of the pad Thai sauce and sauté until warmed through, for about 2 minutes.
Season. Taste and adjust the flavor as needed, adding more tamari for saltiness, lime juice for acidity, maple syrup for sweetness, and red pepper flakes for heat.
Serve. Garnish the pad thai with crushed peanuts and sliced green onions. Serve hot with a wedge of lime on the side of the plate.
Store. Leftover pad thai keeps well in an airtight container in the refrigerator for 3-4 days.
Reheat. Heat a little bit of peanut oil in a large sauté pan. Fry the pad thai until hot, for 2-3 minutes.