8 tablespoons olive oil, divided
1 medium shallot, chopped, divided
2 tablespoons buttermilk, plain yogurt, or crème fraîche
2 tablespoons white wine vinegar
1 teaspoon Dijon mustard
1 teaspoon honey
4 tablespoons finely chopped chives, divided
12 ounces Japanese eggplant (about 2 small), halved lengthwise, sliced crosswise on a diagonal 1/4-inch thick
2 Persian cucumbers, halved lengthwise, thinly sliced crosswise on a diagonal
1/4 cup parsley leaves with tender stems
2 tablespoons fresh lemon juice
1 avocado, cut into 1/2-inch pieces
Heat 1 Tbsp. oil in a large skillet, preferably cast iron, over medium-high. Add half of shallot and cook, stirring often, until tender and slightly charred and crisp around the edges, about 5 minutes; season with salt. Remove skillet from heat.
Whisk buttermilk, vinegar, mustard, honey, and several grinds of pepper in a medium bowl until smooth. Scrape in charred shallot; reserve skillet. Add 3 Tbsp. oil and 2 Tbsp. chives and mix well. Season dressing with salt.
Heat 2 Tbsp. oil in reserved skillet over medium-high. Add half of eggplant slices and arrange in a single layer; season lightly with salt. Cook, without moving, until browned underneath, about 3 minutes. Turn; cook on second side until browned and tender, about 2 minutes. Transfer to a large bowl. Add remaining 2 Tbsp. oil to skillet and repeat with remaining eggplant slices.
Let eggplant cool slightly, then add cucumbers, parsley, lemon juice, half of lemon zest, and 1 Tbsp. chives to bowl. Toss well; season with salt and pepper. Gently fold in avocado.
Transfer to a platter and drizzle with several spoonfuls of dressing (you don’t need to use all of it). Top with remaining lemon zest, shallot, and 1 Tbsp. chives.