In a large mixing bowl, combine chickpeas and 6 quarts water. Let soak at least 8 hours or overnight.
Drain chickpeas through a colander into a non-reactive container. Transfer to a food processor and pulse until broken up into coarse pieces.
In a saucepan, heat oil to 325°F. Fry chickpeas until golden brown and crispy. Transfer to a paper towel-lined sheet tray and let drain. Season with salt. Transfer to a non-reactive container and reserve.
In a pot over medium high heat, combine vinegar, sugar, and salt; bring to a boil. Add eggplant and cook 2 minutes, or until eggplant is slightly translucent. Be careful not to overcook. Drain eggplant and transfer to a baking sheet. Drizzle with olive oil and basil and let stand at room temperature for 1 hour.
Prepare a cold smoker. In a pan, combine all ingredients for smoked vinegar. Place in smoker and cold smoke for 30 minutes.
In a mixing bowl, add tomatoes, Smoked Vinegar, olive oil, and salt. Toss to coat and set aside.
Spread 3 spoonfuls burrata on the bottom of a serving bowl. Season with salt, pepper, and olive oil.
Spoon dressed tomatoes over burrata. Garnish with a few pieces of Pickled Eggplant, a handful of Crispy Chickpeas, and fresh herbs.
