Even when their flavors are complex, Asian dishes don't have to be difficult to make. Preparations for the simpler stir-fries that Thai families enjoy, such as Pad Thai, can be streamlined so that busy stateside families can enjoy them any night of the week.
Bring a large pot of water to a rolling boil. Add the noodles and turn off the heat. Let them stand for 10 minutes, using tongs or two forks to separate the strands as they soften and turn from translucent ivory to white. Drain the noodles, rinse them well in cold water, and drain again. Set them aside.
In a small bowl, stir together the Asian fish sauce, sugar, soy sauce, water, and chili flakes if desired, until the sugar dissolves and everything is well mixed. Set aside.
Heat 1 tablespoon of the vegetable oil in a wok or large skillet over high heat. Add the egg and scramble it as it cooks just until it is no longer runny, about 30 seconds. Transfer the egg to a plate.
Add another tablespoon of oil to the pan and swirl it around. Add the garlic and toss well. Add the chicken and cook it until the edges have mostly changed color, about 1 minute. Toss it well and continue cooking to brown it, about 30 seconds, then push it to the sides. Scatter in the shrimp, spreading them out, and cook until the edges have changed color, about 1 minute. Toss them well. Add the carrot and cook everything about 1 minute longer. Scoop the chicken, shrimp, and carrot into a bowl, leaving as much oil as possible in the pan.
Swirl the last tablespoon of oil in the pan. When it's hot, add the noodles, spreading them to the edges. Cook for 1 minute, until the oil sizzles. Scoop up the noodles and turn them over in a big mass. Cook them another minute, then turn them again.
Pour the sauce mixture around the sides of the pan. When it sizzles, place the cooked chicken and shrimp on the noodles, along with the bean sprouts, scallions, and cooked egg. Gently scoop the noodles from the bottom and turn them over. Continue tossing them to mix in the chicken, shrimp, and egg. Remove the pan from the heat. Add the lime juice and toss the noodles well. Serve the Pad Thai hot or warm, topped with chopped peanuts if you like.