Preheat oven to 450°F. Line a rimmed baking sheet with foil for easy cleanup.
Prick eggplants all over with a fork. Rub with 1 tbsp olive oil and set on the sheet.
Roast 35–40 minutes, turning once, until skins are charred and flesh collapses.
Cool 10 minutes. Split eggplants and scoop the flesh into a colander. Drain 10 minutes, pressing gently.
Mash the eggplant in a bowl until mostly smooth but still a little textured.
Stir in tahini, lemon juice, garlic, cumin, smoked paprika, red pepper flakes, and salt.
Stream in the remaining 2 tbsp olive oil while mixing until creamy and well combined.
Taste and adjust salt or lemon. Swirl into a bowl, drizzle a little oil, and top with parsley.