Tatsoi leaves, an Asian green, impart a subtle mustard flavor to this cold noodle salad, while the mirin, a Japanese rice wine, adds sweetness. Spinach can be substituted for tatsoi.
Combine soy sauce, mirin, sesame oil, lime juice, and ginger in a small bowl; whisk to combine. Set aside.
Bring a large pot of water to a boil. Cook noodles until al dente, 8 to 10 minutes. Transfer to a colander; run under cold water to stop cooking. Drain well.
In a large bowl, combine noodles, basil, tatsoi, and reserved dressing. Toss to combine. Garnish with basil flowers.