Prepare sauce by combining vinegar, sesame oil, miso, ginger, and turmeric in a small bowl; stir with a whisk. Set aside.
Heat vegetable oil in a large skillet over medium-high. Add bok choy and carrots; cook 5 minutes, stirring often, until softened. Stir in rice and soy sauce, and press rice down evenly in the skillet. Cook, undisturbed, until bottom of rice begins to crisp, about 3 minutes. Toss to combine.
Create a large opening in the center of the pan by pushing rice and vegetables to all sides. Pour in eggs and whisk constantly until eggs are scrambled, about 1 to 2 minutes. Toss eggs with rice mixture, and stir in basil.
Divide fried rice evenly between each of 4 plates. Drizzle Miso-Turmeric Vinaigrette over top.
