Fill a large pot with water, salt it, and bring it to a boil to cook the noodles later. Drain the tofu and pat dry with a paper towel. Halve the tofu lengthwise and cut it into 1-inch cubes.
Add the rice noodles to the boiling water and turn the heat off. Let the noodles soak until they’re pliable but not fully tender, about 3 to 5 minutes. Drain and rinse the noodles in a colander under cool water to stop the cooking process. Set aside.
In a small bowl, whisk together the soy sauce, brown sugar, 1 tbsp water, the juice of 1 1/2 of the limes (reserve the other half for garnish), and half of the sambal sauce. Peel and mince the ginger. Rinse and cut the Chinese broccoli into 1-inch pieces.
Place a large nonstick skillet over medium-high heat and add 1 tbsp oil. Once the oil is hot, add the tofu to the pan and season with salt and pepper. Cook, while stirring occasionally, until it begins to brown, about 5 to 6 minutes. Transfer tofu to a plate.
Return the skillet to the heat and add 1 tsp oil. Add the ginger and Chinese broccoli, and a pinch of salt and pepper. Cook until the broccoli is bright green and tender, about 2 minutes. Add the rice noodles and the soy mixture to the skillet. Toss to coat noodles evenly, and cook until sauce has thickened, about 1 to 2 minutes.
Roughly chop the Thai basil. Trim and thinly slice the scallion. Add the tofu and basil to the noodles and cook until the tofu is heated thoroughly about 1 minute. Sprinkle with scallion and serve with the remaining half lime cut into wedges.