Light a grill. Rub the eggplant with olive oil and grill over high heat, turning occasionally, until the skin is charred and the eggplant is very tender, 20 minutes. Let the eggplant cool slightly, then scoop the flesh into a colander and let stand for 10 minutes to drain.
Meanwhile, soak the chiles in boiling water until pliable, about 15 minutes. Drain them and discard the stems and seeds, then transfer the chiles to a blender. Add the eggplant, paprika, cumin, sugar and 1/4 cup of oil and puree. Season with salt and pepper.