Place eggplant directly on a gas burner and roast over medium-low heat. Turn until charred and blistered all over, about 5 minutes per side. Remove from heat, place in a bowl, cover the bowl with plastic wrap, and let cool for 10 minutes (this will make it easier to remove the charred skin).
When the eggplant is cool enough to handle, remove to a cutting board, make a cross-cut to open, and scoop out 1 cup of the flesh into another bowl. Add a pinch of salt and ¼ cup Basic Tahini Sauce and mix. Grate in about ¼ teaspoon garlic, followed by the olive oil, and mix again. Garnish with more Basic Tahini Sauce, pine nuts, cherry tomatoes, salt, sumac, parsley, and more olive oil, and serve. (Note: Video for how to make the Basic Tahini Sauce can be found in Michael Solomonov's Hummus recipe.) To make the Basic Tahini Sauce: Break up the head of garlic with your hands, letting the unpeeled cloves fall into a blender. Add the lemon juice and ½ teaspoon salt. Blend on high for a few seconds until you have a coarse purée. Let the mixture stand for 10 minutes so the garlic can mellow.Pour the mixture through a fine-mesh strainer set over a large mixing bowl, pressing on the solids to extract as much liquid as possible. Discard the solids. Add the tahini to the bowl, along with the cumin and 1 teaspoon salt. Whisk the mixture until smooth; the sauce will lighten in color. Whenever the tahini seizes up or tightens, add ice water bit by bit (about 1.5 cups in total), whisking energetically until you have a perfectly smooth, creamy, thick sauce.