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Prepare the eggplant: Remove the cap and slice it lengthwise into 1/4 inch slices. Lightly salt each of the slices, place them in a colander, and weigh them down with a heavy pan. Let them sit like this for up to an hour. Then rinse the slices and pat them down.
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Lightly coat the slices with olive oil and grill them over medium heat, no more than 3 minutes per side, or until nice grill marks appear. Arrange the grilled eggplant on a serving platter.
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Meanwhile, whisk together the tahini, apple cider vinegar, garlic, almond milk, and salt. Drizzle over the eggplant, then garnish with dill, pomegranate, and flower petals.