Sabich

Make the huevos haminados ahead: Preheat the oven to 200°F [95°C]. Mix all the ingredients with the water in a large ovenproof pot. Cover and bake for at least 8 hours or up to 12 hours.

Remove the pot from the oven. Crack but do not peel the eggs, then return them to the pot with the liquid. Set the pot on the stovetop and cook over high heat, uncovered, until almost all the liquid has evaporated, about 20 minutes (watch closely, the eggs will explode if the pot gets too dry). Cool the eggs on a plate, then peel and slice.

Make the fried eggplant: Stripe the eggplant lengthwise with a vegetable peeler and trim off the ends. Slice into 12 roughly ½-inch (12 mm) thick rounds. Sprinkle each of the eggplant slices on both sides with the salt and drain on a wire rack set on a baking sheet for 1 hour.

Pat the slices dry with paper towels. Put the cornstarch in a shallow bowl. Dredge the eggplant in the cornstarch on both sides and tap off the excess. Place a large skillet over medium heat and coat the bottom with oil. When the oil is hot, fry the eggplant in batches for about 2 minutes per side, or until golden. With a spatula, transfer the eggplant to paper towels to drain. Cool slightly before assembly.

Make the tahini sauce: Nick off a piece of the garlic (about a quarter of the clove) and drop it into the bowl of a food processor. Add the lemon juice to the bowl. Pour the tahini on top, making sure to scrape it all out of the container, and add the cumin and salt. Process until the mixture looks peanut buttery, about 1 minute, then stream in the ice water a little at a time with the motor running. Process until the mixture is smooth and creamy and lightens to the color of dry sand.

Assemble ingredients into a fresh pita and drizzle with tahini on top.