Separate the wide rice noodle sheets so they are not sticking together, cut into 1-inch by 5-inch strips and put them in a large bowl. Pour the hot water over the noodles and let sit for 30 seconds. Drain in a colander and rinse with cold water. Coat the noodles with 1 tablespoon vegetable oil, spread them out on a large baking sheet and set aside.
Whisk together the fish sauce, dark soy sauce, palm sugar and 1/4 cup water in a medium bowl until blended and the sugar is dissolved. Set aside.
Heat 2 tablespoons vegetable oil in a large wok or saute pan over medium-high heat. Add the garlic and cook for 30 seconds, stirring constantly so the garlic does not burn. Add the shrimp and the salt and cook until the shrimp is lightly browned and cooked through, for 3 to 4 minutes. Transfer the shrimp and garlic to a plate.
Add the remaining 2 tablespoons vegetable oil to the wok. Add the baby corn, chiles and bell peppers and cook until the bell peppers are just starting to brown, for 1 to 2 minutes. Turn the heat up to high and add the noodles and the fish sauce/palm sugar mixture. Stir to combine and cook for 1 to 2 minutes. Stir in the grape tomatoes, basil and cooked shrimp and cook until the basil is wilted and the tomatoes are just cooked through, for 1 to 2 minutes.
The pad kee mao can be served either individually or family-style.
This is a quick-cooking dish so it is important to have everything prepped and ready to go before you heat up your wok or saute pan. Keep a small bowl of water nearby so if the wok ever gets too hot, you can add a tablespoon or two of water to cool it down quickly.