Place the dry brown rice noodles in a large bowl and cover with very hot water; let soak for 8-10 minutes until tender but still firm, then drain.
In a small jar, whisk together the tamari, lime juice, coconut sugar, and fish sauce until the sugar is fully dissolved.
Heat the toasted sesame oil in a large wok or non-stick skillet over medium-high heat.
Add the minced garlic and red pepper flakes, sautéing for 30 seconds until fragrant.
Add the shrimp to the pan and cook for 2-3 minutes until they turn pink and opaque, then push them to one side of the pan.
Crack the egg into the empty side of the pan and scramble quickly until just set.
Add the drained noodles and shredded carrots to the pan, pouring the prepared sauce over everything.
Toss all ingredients together for 1-2 minutes using tongs until the noodles are well-coated and the sauce has thickened slightly.
Remove from heat and fold in the bean sprouts and sliced green onions, allowing the residual heat to soften them slightly while maintaining their crunch.
Serve immediately with an extra squeeze of lime if desired.