Preheat a grill or grill pan to medium-high. Cut eggplant lengthwise into 1/2-inch-thick slices, discarding end slices that are mostly peel. Slice onion into 1/2-inch-thick rounds. Cut bell pepper lengthwise into 2-inch-wide slices.
Brush vegetables on both sides with 3 Tbsp. olive oil and grill, working in batches if necessary, until charred on both sides and cooked through, 3 to 5 minutes per side.
When cool enough to handle, coarsely chop vegetables and transfer to a food processor along with 1 Tbsp. olive oil, vinegar, garlic, oregano, salt and pepper. Pulse until mixture is finely chopped with some texture remaining. Taste and season with additional salt and pepper, if necessary. Transfer to a serving bowl.
Preheat oven to 350°F. In a small bowl, stir together paprika, cumin and 1/2 tsp. salt. Cut each pita into 8 triangles. Separate each triangle into 2 pieces. Arrange triangles in a single layer on 2 large baking sheets. Lightly drizzle with remaining 3 Tbsp. olive oil and sprinkle with spice mix. Bake until crisp and golden brown, about 12 minutes. Serve dip at room temperature with pita chips.