Bring vinegar and sugar to boil in saucepan over medium-high heat. Reduce heat to medium-low and simmer until mixture reduces by half, 5 to 6 minutes. Transfer to medium bowl and cool to room temperature.
Whisk in lime juice, ginger, chile, and sesame oil. Toss in cucumbers, scallions, and basil; season with salt and pepper, and let sit for 10 minutes or up to 1 hour. Serve.