Cook the brown rice noodles according to package instructions until al dente, then drain and set aside.
In a small bowl, whisk together the coconut aminos, lime juice, and sambal oelek 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 shrimp to the skillet, seasoning with sea salt and red pepper flakes; sauté until the shrimp are pink and opaque.
Push the shrimp to one side of the pan and crack the egg into the empty space, scrambling it until fully cooked.
Add the cooked noodles, bean sprouts, and shredded carrots to the skillet.
Pour the sauce over the mixture and toss everything together for 1-2 minutes until the vegetables are slightly softened and the noodles are well coated.
Garnish with sliced green onions and serve immediately.