Preheat your grill or oven to 400°F (200°C). Pierce the eggplants several times with a fork to prevent them from bursting. Place them on the grill or a baking sheet and roast for 30-40 minutes, turning occasionally, until the skin is charred and the flesh is soft. Remove from heat and let them cool for a few minutes.
Once cool enough to handle, cut each eggplant in half and scoop out the tender flesh into a mixing bowl, discarding the skin.
In the mixing bowl with the eggplant, add the tahini, lemon juice, minced garlic, cayenne pepper, kosher salt, and black pepper. Using a food processor, blend the mixture until smooth and creamy. Taste and adjust seasoning as needed.
Transfer the Baba Ghanoush to a serving bowl. Drizzle with olive oil and sprinkle with paprika for an extra touch. If desired, garnish with chopped fresh parsley.