Preheat the oven to 450 degrees.
Place eggplant in a large mixing bowl and add salt, pepper, and 1 1/2 tablespoons olive oil; toss the eggplant to coat.
Divide the eggplant between 2 large roasting pans (9 by 12-inch works well) or place on one large rimmed baking sheet (like a half-sheet pan). Spread eggplant pieces evenly in one layer so they aren’t crowded. Roast for 20 minutes, stirring two to three times, until soft and well browned. Remove from oven and set aside.
While the eggplant is roasting, heat the remaining 1 1/2 tablespoons of olive oil in a medium stockpot over medium heat. Add the onion, garlic, and tomatoes and cook, stirring occasionally, for 8 to 10 minutes or until the onion is soft.
Stir in the roasted eggplant and cook for 5 minutes. Add the thyme, 1 tablespoon chives, and 3 cups vegetable broth. Bring to a boil, reduce heat, and simmer, stirring occasionally, until eggplant is very soft, around 10 to 12 minutes.
Stir in vinegar.
Remove from heat. Let sit for around 2 minutes, then purée with an immersion blender. Alternatively, cool soup for 5 to 7 minutes, and then transfer to a blender or food processor in batches and purée until smooth. Return soup to pot and season to taste with salt and pepper. Stir in more vegetable broth (up to 1 cup) if soup is too thick.
Heat over medium-low heat, stirring frequently. Spoon into individual bowls, garnishing with remaining 1 tablespoon chopped chives.