Place the brown rice noodles in a large bowl and cover with very hot water, soaking for 8-10 minutes until tender but firm, then drain.
In a small jar, whisk together the tamarind paste, coconut aminos, fish sauce, and red pepper flakes to create the Pad Thai sauce.
Heat the avocado oil in a large wok or non-stick skillet over medium-high heat.
Add the shrimp to the wok and sear for 2 minutes per side until pink and opaque, then remove and set aside.
Push any remaining oil to the side, crack the egg into the pan, and scramble quickly until just set.
Add the drained noodles, shredded carrots, and the prepared sauce to the wok, tossing constantly for 2 minutes to coat the noodles evenly.
Return the shrimp to the pan along with the bean sprouts and sliced green onions, tossing for 30 seconds until the sprouts just begin to soften.
Transfer to a plate and garnish with crushed peanuts and a fresh lime wedge before serving.