Cut the eggplant into ¾-inch slices, and generously season them with salt. Place the slices in a colander, overlapping as necessary. Let stand 15 to 30 minutes, then pat dry with paper towel (this step helps to remove bitterness from the eggplant prior to grilling).
Liberally brush cut sides of eggplant with olive oil (about 4 tablespoons total). Place on a grill and cook, turning once, until tender, about 4 minutes a side.
Cut the cherry tomatoes in half. Chop the dill, basil, and cilantro. When the quinoa is done, mix it together with the tomatoes, herbs, feta cheese crumbles, white wine vinegar, 1 tablespoon olive oil, and the kosher salt.
To serve, place two to three eggplant slices on a plate and spoon herbed quinoa and tomato mixture on top.