Charred Broccoli Salad with Eggplant Purée

Name: Charred Broccoli Salad with Eggplant Purée
Ingredients: 1 medium eggplant, cut in half lengthwise; 1/2 cup olive oil, divided, plus more for brushing; 1 teaspoon kosher salt, plus more; Freshly ground black pepper; 2 bunches broccoli, florets separated from stems, stems peeled and shaved lengthwise on a mandoline; 2 Fresno chiles, halved lengthwise, thinly sliced; 1 tablespoon sugar; 1/2 cup white wine vinegar; 2 tablespoons coriander seeds; 1/4 cup seasoned rice vinegar; 3 tablespoons fresh lemon juice, divided; 2 tablespoons malt vinegar; 1 tablespoon agave nectar; 1 tablespoon tahini; 1/2 cup unsalted, roasted cashews, chopped; 1/4 cup cilantro leaves with tender stems; A spice mill or a mortar and pestle