In a mixing bowl, combine the noodles with the 2 teaspoons soy sauce and toss gently a few times. Set aside.
Using a small wire whisk or chop sticks, dissolve the cornstarch in the water and set aside.
Heat the 2 tablespoons oil in a large nonstick fry pan over moderate heat and tilt pan to completely coat the entire cooking surface. Add the noodles, and turning only once or twice, brown slightly on both sides, 3 to 5 minutes. Remove from heat and set aside.
In another fry pan, heat the 1 tbsp oil over moderate heat. Wait for the pan to get very hot and add the garlic, chilies, and soybeans. Stir-fry until fragrant, about 1 minute. Add the chicken and toss to pick up the seasonings, 2 to 3 minutes. Add the oyster sauce, the 1 teaspoon soy sauce, fish sauce, sugar, chicken stock, and vinegar. Wait for sauce to boil, then add the broccoli. Stir in the cornstarch mixture, adding 1 tbsp at a time until sauce slightly thickens. Add the tomatoes and cook until vegetables and chicken are done, about 3 more minutes.
To serve, place the warm noodles on a plate and top with the stir-fry. Garnish with cilantro and a sprinkling of white pepper. Serve with Thai chili dipping sauce.