Heat a charcoal grill or indoor grill pan to high.

Remove the top and bottom of the eggplant and stand it up on a cutting board. Slice the eggplant length-wise and thin as you can.

In a small mixing bowl, combine the sumac and olive oil. Brush each piece of eggplant on both sides.

Grill the eggplant on both sides, rotating 90 degrees halfway through to get a nice crosshatch, until soft and charred, about 2 minutes per side.

Arrange the grilled eggplant on a platter. Add the lemon juice, mint, capers, and salt to the remaining olive oil mixture and stir to combine. Drizzle the eggplant with the caper mixture. Serve immediately or at room temperature.