Make the pickled turnips: At least four days in advance, prepare the turnips.

Put the water and salt in a medium saucepan, heat over medium heat until very hot but not boiling, and stir until the salt has completely dissolved. Remove from the heat and let the salt water cool completely, then stir in the vinegar.

Put the turnips, beet, and garlic into a large clean glass jar or other nonreactive container with a tight-fitting lid, pour in the brine, and seal the jar.

Let the pickles sit at room temperature for 4 to 6 days, then refrigerate.

Make the eggplant: Lay the eggplant rounds in a single layer on a wire rack set over a baking sheet. Sprinkle the exposed sides with 1 teaspoon of the salt, flip the rounds over, and sprinkle the other sides with the remaining 1 teaspoon salt. Let stand for at least 20 minutes and up to 1 hour.

Preheat the oven to 425°F.

Using paper towels, thoroughly wipe the salt and moisture from the eggplant slices and pat them dry. Generously brush both sides of the rounds with olive oil and lay them on a baking sheet in an even layer; use two baking sheets if necessary.

Roast the eggplant for 20 minutes, then flip the slices and continue roasting until they are golden brown and tender all the way through, another 20 minutes or so. Remove from the oven and set aside.

Cook the potatoes: Fill a large pot with cold water. Add the salt and potatoes. Bring to a boil over high heat, then reduce the heat to medium-high and cook the potatoes at an active simmer until they are fork-tender, about 20 minutes. Drain the potatoes and set aside until cool enough to handle.

Peel the potatoes using a knife and then slice into ¼-to ½-inch pieces. Transfer to a plate and set aside.

Boil the eggs: Fill a large bowl with ice water and set aside. Bring a medium saucepan of water to a boil over medium-high heat. Gently add the eggs to the boiling water, using a slotted spoon. Boil the eggs for 7 minutes for soft-boiled, jammy eggs, or for 12 minutes for hard-boiled eggs. Immediately transfer the eggs to the ice bath and let cool completely.

Peel the eggs and cut them into ¼-inch slices. Set aside.

Make the tahini sauce: Put the tahini paste in a medium bowl and slowly add ⅓ cup of the ice water, whisking until well blended. Whisk in the remaining ⅓ cup ice water until the mixture is blended and all the water is absorbed. The tahini may stiffen at first, but eventually the sauce will develop a creamy consistency. Add the lemon juice and salt and whisk again to combine.

Make the chopped salad: Finely chop the cucumbers and tomatoes into small cubes (about ¼ inch). Chop the red onion into small dice (about ¼ inch). Put the cucumbers, tomatoes, and onion in a large salad bowl and add the parsley, if using.

Just before serving, add the lemon juice and toss to distribute. Add the olive oil, salt, and pepper and toss again to mix well. Taste and adjust the seasoning if needed.

Create the sabich spread: Arrange the pickled turnips, potatoes, eggs, and chopped salad in separate serving bowls and place the eggplant slices and pita on separate platters. Put the tahini sauce, parsley sprigs, and amba in bowls.

Invite diners to build their own sabich sandwiches, choosing their favorite ingredients.