Combine eggplants, bell pepper, onion, and garlic in a multi-functional pressure cooker (such as Instant Pot®). Add water, cumin, oregano, and salt. Close and lock the lid. Select high pressure according to manufacturer’s instructions; set timer for 10 minutes. Allow 10 to 15 minutes for pressure to build.
Meanwhile, heat butter in a small saucepan over medium heat. Add flour; cook and stir until thick, 3 to 5 minutes. Cook 1 minute more, stirring roux constantly. Add white beans to roux and mix.
Release pressure carefully using the quick-release method according to manufacturer’s instructions, about 5 minutes. Unlock and remove the lid.
Scoop cooked eggplant and vegetables out of pressure cooker using a slotted spoon or pasta server, including as little water as possible, and transfer to a blender. Add roux-bean mixture and blend until smooth. Add lemon juice, tahini, and oil.