Prepare the brown rice noodles by soaking them in hot water according to the package instructions until al dente, then drain and set aside.
In a small bowl, whisk together the lime juice, coconut aminos, fish sauce, and chili paste to create the pad thai sauce.
Heat the avocado oil in a large wok or non-stick skillet over medium-high heat.
Add the minced garlic and shrimp to the pan, seasoning with sea salt and black pepper, and 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 quickly until just set.
Add the cooked noodles, bean sprouts, and shredded carrots to the wok.
Pour the prepared sauce over the ingredients and toss everything together for 1-2 minutes until the vegetables are slightly softened and the sauce is well-distributed.
Garnish with sliced scallions and crushed peanuts before serving warm.