In a small bowl, whisk the vinegar with the oregano, agave, and a generous pinch of salt and pepper. While whisking constantly, drizzle in the oils until incorporated. Season with salt and pepper as needed.
In a small bowl, mix together all of the dukkah ingredients; set aside.
Light a grill or preheat a grill pan.
In a large bowl, toss the tomatoes with one tablespoon of olive oil; season with salt and pepper. Place the tomatoes on a skewer, leaving a few inches on each end for handling. Transfer to a large rimmed baking sheet.
In the same large bowl, gently toss the eggplant and romaine with two tablespoons of the olive oil and season with salt and pepper. Transfer to the baking sheet with the tomatoes.
Brush both sides of the pita halves with the remaining tablespoon of olive oil; Transfer to the baking sheet.
Grill the tomatoes and eggplant over medium-high heat, turning occasionally, until the tomatoes are charred in spots and beginning to burst and the eggplant is lightly charred and tender, about five minutes for the tomatoes and about ten minutes for the eggplant; Transfer to the baking sheet.
Grill the romaine and pita halves over medium-high heat, turning occasionally, until the lettuce is lightly charred on the outside, but raw within, and the pita is crisp, about three to five minutes; Transfer to the baking sheet.
Roughly chop the grilled romaine and transfer to a large bowl. Cut the eggplant into bite-size pieces; add to the bowl. Remove the tomatoes from the skewers and add them to the bowl. Break the grilled pita into bite-size pieces and add to the bowl. Add the radishes, cucumbers, red onion, herbs, and olives.
Plate salad and drizzle with some of the vinaigrette. Sprinkle generously with the dukkah.