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 bowl, whisk together the tamarind paste, coconut aminos, and fish sauce to create the Pad Thai sauce base.
Heat the avocado oil in a large skillet or wok over medium-high heat and add the shrimp, searing for 2 minutes per side until pink and opaque.
Push the shrimp to one side of the pan, crack the egg into the empty space, and scramble quickly until just set.
Add the drained noodles and the prepared sauce to the skillet, tossing everything together for 1-2 minutes until the noodles are well-coated and hot.
Fold in the bean sprouts, sliced green onions, and red pepper flakes, removing from heat immediately to keep the sprouts crisp.
Transfer to a plate and garnish with crushed peanuts and a generous squeeze of fresh lime juice before serving.