Cook the rice noodles according to the package directions, stopping while they are still slightly firm to the bite, since they will continue cooking in the sauce. Rinse the noodles under cold water, drain well, and toss with the toasted sesame oil. Set aside.

In a medium mixing bowl, whisk together the brown sugar, soy sauce, fish sauce, lime juice, rice vinegar, peanut butter, chili paste, dried basil, coriander, ginger, and black pepper until the sugar is dissolved and the sauce is smooth. Set aside.

Meanwhile, heat 1 tablespoon of the vegetable or peanut oil in a large nonstick skillet or wok over medium-high heat. Add the chicken and let it sear undisturbed for 1 minute, then stir-fry until just cooked through. Transfer the chicken to a plate and wipe out the pan.

Return the skillet to medium-high heat and add the remaining 1 tablespoon oil. Add the bell pepper and shallots and saute for 1 minute. Add the carrots and garlic and cook for 1 more minute. Reduce the heat to medium, pour in the beaten eggs, and stir constantly until softly scrambled.

Pour the sauce into the skillet and add the noodles, then increase the heat to medium-high. Toss everything together until evenly coated and cook, stirring, until the noodles are chewy-tender, about 1 to 2 minutes. Fold in the cooked chicken, bean sprouts, green onions, and peanuts, and heat through.

Taste the pad thai and add an extra tablespoon of lime juice if you prefer more tang, plus more chili paste if you want additional heat. Sprinkle with cilantro and serve right away.