Preheat the grill to medium-high heat (~400ºF/205ºC). Poke holes in eggplant skin, using a toothpick or skewer. Place eggplant on grill, and cook for 15-20 minutes, turning every few minutes, until eggplant skin has been blackened and eggplant is soft.
Remove eggplant to a strainer and allow to cool and any liquid to drain out while cooling.
Add the shredded garlic, tomatoes, basil, olive oil, and paprika to a bowl and stir.
Once the eggplant has cooled, remove and discard the skin. Cut the eggplant in quarters and place back int the strainer to drain for 5 more minutes. Slice the eggplant into small pieces, and add to the bowl with the tomato mixture. Stir, then season with salt and pepper to taste. Serve with pieces of baguette or crostini.