Preheat the oven to 400 degrees F.
On a sheet pan, toss the eggplant, tomatoes and garlic cloves with 1 tablespoon olive oil, 1 teaspoon kosher salt and 1/2 teaspoon black pepper. Spread everything into a single layer, arranging the tomatoes cut side up.
Roast for 25 minutes until the eggplant is starting to brown at the edges and the tomatoes are wrinkling. Scatter the halloumi on the pan and continue roasting for 10-15 minutes until the cheese is lightly golden.
For the sauce, squeeze the roasted garlic cloves out of their skins into the bowl of a food processor. Add the parsley, lemon juice, tahini, 1/4 teaspoon kosher salt, 1/4 teaspoon black pepper and 1/4 cup olive oil. Puree until the sauce is smooth and combined.
Spoon the about half the sauce onto the eggplant, tomatoes and halloumi on the sheet pan, gently tossing to coat the ingredients. Add more sauce as desired or serve the rest in a bowl on the side.
Serve with cooked grains.