Fold in the parmesan, and 1 teaspoon salt. Seasoning to taste with pepper and additional salt as necessary.
Grill the eggplant: Prepare a medium-high charcoal or gas grill.
Brush the eggplant rounds on both sides with oil, sprinkle generously with salt, and arrange on the grill. Cook for 2-3 minutes or until golden-brown. Flip, cook for 2-3 more minutes. Transfer to a cutting board and slice into cubes.
Meanwhile, bring a large pot of salted water to a boil. Cook the pasta until al dente; drain.
Gently toss together the hot pasta, eggplant, and cherry tomatoes. Add the pesto to taste (I used about 1 cup, with about 1 cup leftover). Garnish with the basil chiffonade and a few grinds of black pepper. Serve hot or at room temperature.
Notes
About 1 cup of store-bought pesto can be substituted for homemade in a pinch. Let leftovers come up to room temperature for an hour; don't reheat.
Recipe by A Modest Feast at http://www.amodestfeast.com/2016/06/29/pesto-pasta-grilled-eggplant-tomatoes/