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Put the noodles in a large bowl and cover with very hot water. Let soak until just pliable, about 15 minutes (or according to package directions). Drain the noodles in a colander, shaking off any excess water.
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Meanwhile, in a small bowl, whisk the soy sauce with the brown sugar, tamarind paste and Sriracha.
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In a large nonstick wok or skillet, heat 1 tablespoon oil until shimmering. Add the tofu and cook until lightly browned on both sides. Transfer the tofu to a plate. Heat the remaining 1 tablespoon of oil. Add the garlic, shallots and carrots and cook over high heat, stirring occasionally, until lightly browned, about 5 minutes. Add the noodles and scallions and stir-fry until heated through, about 2 minutes.
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Scrape the noodles to one side of the pan and add the eggs. Cook, stirring occasionally, until nearly set, about 1 minute. Toss everything together. Add the sauce and tofu and stir-fry until the noodles are evenly coated and the sauce has thickened slightly, 2 to 3 minutes. Transfer the pad Thai to a platter. Garnish with the bean sprouts and serve with the lime wedges.
Notes
Tamarind paste is available from Indian, Asian and Latin markets.