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 tamari, fish sauce, lime juice, and coconut sugar to create the Pad Thai sauce base.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat, then add the minced garlic and red pepper flakes, sautéing for 30 seconds.
Add the shrimp to the skillet and cook for 2-3 minutes until pink and opaque, then push them to one side of the pan.
Crack the egg into the empty side of the pan, scrambling it quickly until just set, then mix it in with the shrimp.
Add the drained noodles and the prepared sauce to the pan, tossing vigorously for 1-2 minutes until the noodles are well-coated and the sauce has thickened slightly.
Fold in the mung bean sprouts and sliced green onions, cooking for just 30 seconds more to retain their crunch.
Remove from heat and serve immediately, garnished with fresh cilantro and an extra squeeze of lime if desired.