Soak the brown rice noodles in a bowl of very hot water for 10 minutes until softened, then drain and set aside.
In a small bowl, whisk together the tamari, lime juice, honey, fish sauce, and red pepper flakes to create the sauce.
Heat the avocado oil in a large skillet or wok over medium-high heat.
Season the shrimp with sea salt and black pepper, then add them to the skillet and sear for 2 minutes per side until pink and opaque.
Push the shrimp to the outer edges of the pan, crack the egg into the center, and scramble quickly until just set.
Add the drained noodles, shredded carrots, and the prepared sauce to the pan, tossing everything together for 2 minutes to coat.
Stir in the bean sprouts and sliced green onions, cooking for 1 minute until the sprouts are slightly wilted.
Transfer the Pad Thai to a plate and garnish with the crushed peanuts before serving warm.