Brush eggplant with the remaining 1 tablespoon oil. Grill, turning once, until tender and charred in spots, about 4 minutes per side. Grill sausage until charred and cooked through, 8 to 10 minutes. Let the eggplant and sausage cool for 10 minutes. Chop the eggplant into bite-size pieces and thinly slice the sausage. Add to the tomatoes along with basil.