Preheat your oven to 400°F (200°C) with a rack in the middle.
Place the whole eggplant on a baking sheet and roast for 1 hour, until the skin is charred and the inside is completely tender.
Let the eggplant cool until you can handle it.
Slice it open, scoop the soft pulp into a bowl, and discard the charred skin.
Add the peeled garlic cloves to a food processor and pulse until finely chopped.
Add the eggplant pulp, tahini, kosher salt, cumin, and half of the lemon juice to the food processor.
Process until smooth, slowly drizzling in the 2 tbsp (30 ml) of olive oil through the feed tube to create a creamy emulsion.
Taste the dip.
Add the black pepper and remaining lemon juice or more salt as needed to achieve your desired flavor.
Spread the baba ghanouj onto a serving plate, making a decorative swirl with the back of a spoon.
Garnish with a generous drizzle of extra-virgin olive oil, a sprinkle of paprika, and the chopped fresh parsley.
Serve immediately with warm pita wedges for dipping.
After roasting, place the eggplant pulp in a fine-mesh strainer for 10-15 minutes to drain excess water. This prevents a runny dip and concentrates the flavor.