Heat 1 tablespoon of the oil in a large skillet over medium  high heat. Add half of the shallot or onion, and cook, stirring often, until tender and slightly crisp around the edges (about 5 minutes). Season with salt. Remove skillet from heat. Whisk the buttermilk, vinegar, mustard, honey, and several grinds of pepper in a medium bowl until smooth. Add the cooked shallots (or onions). Add 3 tablespoons olive oil and 2 tablespoons chives and mix well. Season with salt.

Heat 2 tablespoons oil in the same skillet over medium high heat. Add half of the eggplant slices and arrange in a single layer; season lightly with salt. Cook, without moving, until browned underneath, about 3 minutes. Turn; cook on the second side until browned and tender, about 2 minutes. Transfer to a large bowl. Add the remaining 2 tablespoons olive oil and cook the remaining eggplant. 

Let the eggplant cool slightly, then add the cucumbers, parsley, lemon juice, half the lemon zest and 1 tablespoon chives to the bowl. Toss well. Season with salt and pepper. Gently fold in the avocado. Transfer to a platter and drizzle with several spoonfuls of dressing (you don’t need to use all of it). Top with the remaining zest, shallot and 1 tablespoon of chives.