Fattoush with Halloumi

5 tablespoons olive oil, plus more for grill
2 scallions
1 jalapeño
1/2 cup halved pitted Castelvetrano or other green olives
3 tablespoons salted, roasted pistachios
3 tablespoons fresh lemon juice
1 tablespoon white wine vinegar
Kosher salt, freshly ground pepper
1 tablespoon dried thyme
1 tablespoon toasted sesame seeds
1/4 teaspoon garlic powder
2 six inch pitas
2 medium eggplants, halved lengthwise (or crosswise if using 1 large eggplant)
2 tablespoons olive oil, plus more for grill
Kosher salt
1 eight ounce package Halloumi cheese
2 large Persian cucumbers or 1 small English hothouse cucumber
1 pound tomatoes, halved, cut into wedges if large
1/2 cup torn mint leaves
1/4 cup dill sprigs

Dressing:
Prepare a grill for medium heat; oil grate.
Grill scallions and jalapeño, turning once, until lightly blistered and crisp-tender,
about 2 minutes for scallions and 4 minutes for jalapeño.
Transfer to a cutting board and let cool slightly.
Slice open jalapeño and scrape out seeds (unless you like things very spicy); discard.
Coarsely chop chile and scallions.
Mix in a medium bowl with olives, pistachios, lemon juice, vinegar, and 5 Tbsp. oil;
season dressing with salt and pepper.
Dressing can be made 1 day ahead. Cover and chill.
Bring to room temperature before serving.
Salad:
Mix thyme, sesame seeds, and garlic powder in a small bowl.
Lightly coat pitas and eggplants with 2 Tbsp. oil;
season with salt and rub with thyme mixture.
Grill, turning occasionally and moving to a cooler part of grill if needed to avoid scorching, until pitas are golden and crisp and eggplants are browned and tender, 5 minutes for pitas, and 8–10 minutes for eggplants. Transfer to a platter and let cool slightly.
Meanwhile, grill Halloumi until charred and soft, about 2 minutes per side.
Transfer to platter with pitas and eggplants.
Tear pitas and Halloumi into chunky pieces, then cut eggplants into bite-size pieces.
Transfer to a large bowl and add cucumbers, tomatoes, and dressing.
Give everything a good toss to bring it all together; season with salt.
Top with mint leaves and dill sprigs.

Note:
Halloumi cheese can be found in Greek markets, natural foods and specialty foods stores, and some supermarkets.