Heat a grill to medium. Brush the bell pepper with some of the canola oil and season with salt and pepper. Brush the eggplant slices on both sides with more of the canola oil, season with salt and pepper.
Grill the eggplant until charred on the first side, about 3 minutes. Turn and continue grilling until tender, another 3 to 4 minutes. Transfer the eggplant to a cutting board. Grill the bell pepper, turning occasionally, until charred all over and tender, about 15 minutes. Transfer to a bowl, cover tightly with plastic wrap, and let steam while you make the eggplant puree.
Smash the garlic cloves, sprinkle them with salt, and mash and smear them to a paste using the side of a knife. Remove the skin from the eggplant and transfer the flesh to a food processor. Add the garlic paste, tahini, yogurt, 2 tablespoons of the olive oil, and the lemon zest, oregano and smoked paprika. Process until smooth and thick. Add salt to taste. Transfer to a serving bowl and let sit for at least 15 minutes to allow the flavors to meld. Peel, seed and dice the bell pepper.
Drizzle the remaining 2 tablespoons olive oil over the dip. Top with the diced peppers and the chopped parsley. Serve with warm pita or lavash.