Place the dry brown rice noodles in a large bowl and cover with very hot water. Let soak for 20-30 minutes until flexible but still firm (al dente), then drain and set aside.
In a small bowl, whisk together the tamarind paste, tamari, fish sauce, honey, and red pepper flakes to create the Pad Thai sauce.
Heat the toasted sesame oil in a large wok or non-stick skillet over medium-high heat. Add the shrimp and minced garlic, searing for 2 minutes per side until the shrimp are pink and opaque.
Push the shrimp to one side of the wok. Crack the egg into the empty space and scramble quickly with a spatula until just set.
Add the drained noodles and the prepared sauce to the wok. Toss everything together vigorously for 1-2 minutes until the noodles absorb the sauce and soften completely.
Fold in the bean sprouts and sliced green onions, cooking for only 30 seconds to maintain their texture.
Remove from heat and transfer to a plate. Garnish with crushed peanuts and serve with a fresh lime wedge to squeeze over the top.