Preheat a grill or grill pan to medium-high and lightly brush the grates with olive oil.
Season the eggplant slices all over with salt. Using your hands gently press excess moisture from the eggplant, then brush generously with olive oil. Grill eggplant, turning occasionally until tender and lightly charred in places, about three to four minutes per side, then remove from heat and place in an airtight container once cooled.
In another airtight container, combine the tomatoes with the basil, scallion, one tablespoon olive oil, and vinegar. Season with salt.
Spoon the tomato-basil sauce over the eggplant and serve with quinoa.