Bring a pot of water to a boil and cook the soba noodles according to package directions, then drain and set aside.
In a small mixing bowl, whisk together the tamari, lime juice, chili garlic sauce, minced garlic, and grated ginger to create the sauce.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat.
Season the shrimp with sea salt and black pepper, then add them to the skillet and sauté until they are pink and opaque, about 2 minutes per side.
Add the shredded carrots and bean sprouts to the skillet with the shrimp, sautéing for an additional 2 minutes until the vegetables are slightly softened but still crisp.
Add the cooked soba noodles and the prepared sauce to the skillet, tossing everything together with tongs until well-combined and heated through.
Remove from heat, garnish with sliced green onions, and serve immediately.