Pierce the eggplant skins in several places with a fork. Grill outside or set the eggplants on a baking sheet and roast until soft and the skin is charred, 30 to 45 minutes, turning a few times for even roasting.

When done, cut off the stems and peel the eggplants. Cut a slit along the side of each eggplant and transfer the eggplants to a strainer for a couple of minutes to allow the juices to drain.

Finely chop the eggplants with a knife until they form a smooth puree. (This traditionally better done with a wooden spoon if available). Add the eggplant puree to a bowl and stir in the olive oil and lemon juice until well-blended; taste and add more olive oil and lemon juice if desired. Add the onion and mix in the mayonnaise, adding more if needed. Season with salt and pepper. Garnish with dill and refrigerate for at least one hour to chill.