Using a mandoline, thinly slice the zucchini and eggplant into rounds. Season generously with salt and let sit for about 10 minutes to draw out excess moisture. Place the slices on a clean kitchen towel or paper towel and pat thoroughly dry.
In a bowl, whisk together the flour, cornstarch, water, and a pinch of salt until a smooth batter forms.
Heat a generous drizzle of olive oil in a large skillet over medium heat. Dip the zucchini and eggplant slices into the batter, then carefully place them in the hot oil, a few at a time. Cook for about 2 minutes per side, or until golden and crispy. Transfer to a paper towel-lined plate.
In a small bowl, combine the honey and fig balsamic vinegar.
In another bowl, combine the Greek yogurt, mustard, lemon zest, lemon juice, fresh basil, and a drizzle of basil olive oil. Season with salt and pepper and mix well.
To serve, drizzle the crispy zucchini and eggplant chips with the honey and fig balsamic vinaigrette and serve with the yogurt sauce on the side.
