Soak noodles following package instructions for stir fry; drain and set aside. Thaw shrimp (if needed); peel, devein, and remove tails (wash hands). Beat eggs and set aside. Thinly slice shallots, red chili, and cabbage. Cut green onions into 2-inch pieces; chop cilantro, basil, and mint.
Heat large sauté pan (or wok) on high for 3–4 minutes. Place 1 tablespoon canola oil in pan; when oil is just beginning to smoke, carefully add shrimp and cook 1–2 minutes, stirring continuously, until just pink and opaque. Remove shrimp from pan.
Add another tablespoon oil to same pan, then add egg and cook until just set; remove from pan.
Place remaining 1 tablespoon oil in pan, then add garlic, shallot, and chile. Cook 1–2 minutes, stirring continuously until fragrant. Add noodles, cabbage, and green onions to pan and cook 1–2 minutes until cabbage wilts. Add pad Thai sauce, soy sauce, and squeeze 1 lime over pan; cook 1–2 minutes until sauce is boiling and coating noodles.
Return shrimp, eggs, and 1 cup bean sprouts to pan and cook 1–2 more minutes until shrimp are heated through. Stir in cilantro, basil, mint, and sesame oil. Serve garnished with bean sprouts, peanuts, and remaining 1 lime cut in wedges.