Preheat an outdoor grill for medium heat and lightly oil the grate.

Brush cut sides of eggplant and tomatoes with 2 tablespoons olive oil.

Place eggplants and tomatoes, cut sides down, on the preheated grill. Cook eggplant for 4 minutes, then flip and grill until tender, about 10 minutes more. Cook tomatoes until very tender, about 5 minutes per side. Transfer eggplant to a cutting board and tomatoes to a food processor.

Scrape eggplant pulp from the skins. Discard skins and place pulp in the food processor with tomatoes. Add tahini, parsley, and garlic; pulse until mostly smooth. Season with salt and pepper.

Transfer to a serving bowl. Top with feta cheese and sesame seeds.