Step 1

Place a rack in upper third of oven; preheat to 400°. Score cut sides of eggplants with a sharp knife. Rub with 2 Tbsp. oil and season with salt. Roast, skin side down, on a large rimmed baking sheet until tender but not browned, 22–28 minutes.

Step 2

Meanwhile, whisk ginger, miso, tamari, vinegar, sugar, and remaining 4 Tbsp. oil in a medium bowl until smooth. Set 3 Tbsp. glaze aside in another medium bowl.

Step 3

Increase oven temperature to 450°. Spoon remaining glaze over cut sides of eggplants. Roast until glaze is browned and bubbling, 12–15 minutes. Let cool slightly.

Step 4

While the eggplants are cooling, whisk lime juice into reserved glaze. Add cucumbers, scallions, grains, and basil and toss to coat.

Step 5

Divide eggplants among plates; spoon grain salad over.