Place the brown rice noodles in a large bowl and cover with very hot water; let them soak for 8-10 minutes until tender but firm, then drain.
In a small jar, whisk together the coconut aminos, lime juice, fish sauce, honey, and red pepper flakes to create the Pad Thai sauce.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat.
Add the minced garlic and white parts of the green onions, sautéing for 30 seconds until fragrant.
Add the shrimp to the skillet and cook 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 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 mung bean sprouts and the remaining green onion tops, cooking for just 30 seconds to maintain their texture.
Serve immediately topped with crushed peanuts and an extra squeeze of lime.