Fire up your charcoal grill or set an indoor grill pan over a high flame.

Brush the eggplant slices on both sides with olive oil and season with salt.

Grill the eggplant on both sides until the flesh is charred and very soft, about 3 minutes per side, depending on how hot your grill is. Remove the eggplant to a plate to cool.

In a small food processor, puree the tahini, lemon juice, garlic, and ½ teaspoon of salt. Roughly chop the eggplant and add it to the processor. Pulse until the eggplant is coarsely chopped. I like my baba a little bit on the smoother side, so feel free to puree completely if you like, and add a glug of olive oil if the mixture is too thick. Taste for seasoning.

Spoon the baba into a bowl and garnish with fresh parsley and a drizzle of olive oil, and serve alongside crackers or pita chips.