Rinse both eggplant and pat dry. Prick each eggplant all over with a fork.
Pre-heat grill over medium-high heat. Place the eggplant whole on the grill and close the lid. Cook for 30-40 minutes, rotating occasionally with tongs to eggplant cooks evenly, or until eggplant are blackened and collapsed.
Remove eggplant from grill and let sit for 15-20 minutes until cool enough to handle.
With your fingers, open the eggplant and scoop all the soft insides into a bowl. Mash the cooked eggplant "meat" with a fork until mashed and no large chunks remain.
Add the tahini, crushed garlic, lemon juice, and salt and pepper to the eggplant and stir until well combined. Make sure to season well with salt, adjusting amount to taste.
Cover the dip and chill for several hours to let the flavors come together and open up. Adjust seasoning as needed after it chills, i.e. add more lemon, tahini, salt and pepper. Some like this dip more lemony, some with more tahini (me!) Adjust to your particular taste.
To serve, scoop the dip into a serving dish. Sprinkle topped parsley over top and a drizzle of olive oil.
Serve with warm pita bread, fresh veggies, or hearty crackers.