Combine the tahini, lemon juice, garlic and cumin in the bowl of a food processor and pulse until combined. Add water as needed to create a smooth sauce. Season to taste with salt and pepper. Set aside.
Preheat the broiler and lightly oil a baking sheet.
Cut the eggplant into 1/2-inch-thick slices. Brush 2 tablespoons oil on both sides of the eggplant slices and transfer to the baking sheet. Broil the eggplant 5 to 6 inches from the heat until golden and cooked through, flipping halfway through, about 10 minutes.
To serve, arrange the eggplant on a serving platter and drizzle some of the tahini sauce over the eggplant. Sprinkle the pomegranate seeds over the eggplant.