Preheat the broiler to high and position a rack 4 to 6 inches beneath it.
Pierce the eggplant all over with a fork and place on a rimmed baking sheet. Broil the eggplant, watching carefully and turning every 3 to 5 minutes to prevent burning, until charred on the outside and slightly collapsed, about 15 minutes total. Let the eggplant cool for 10 minutes.
Peel and discard the skin and scoop the flesh into a colander set over a bowl. Press on the eggplant gently with the back of a large spoon and let any excess moisture drain for 5 to 10 minutes. Discard the liquid that accumulates in the bowl.
In a mixing bowl, combine the eggplant with the garlic, salt, oil, yogurt and lemon juice. Chill, covered, for one hour to allow the flavors to meld. Just before serving, stir in the mint and serve with the naan.