Heat a large nonstick skillet over medium-high heat and add the oil. Add the eggplant rounds and season with 1/4 teaspoon salt. Cover and cook until brown on the bottoms, about 4 minutes. Reduce the heat to medium-low and, working quickly, flip each eggplant round and top with a dollop of hummus and a cherry tomato quarter, rounded-side down. Cover and cook until heated through and the bottoms are golden brown, about 7 minutes.
Transfer to a platter using a spatula. Sprinkle with the parsley and lemon zest and serve.