How to Make It
Cook pasta according to package directions, omitting salt and fat. Add green beans during last 3 minutes of cooking. Reserve 1 cup of the cooking liquid; drain.
Meanwhile, heat oil in a large skillet over medium-high. Add eggplant, and cook, stirring occasionally, until tender, 4 to 5 minutes. Add garlic; cook until fragrant, 1 minute. Add half of tomatoes; cook until juices start to release, about 2 to 3 minutes.
Add wine; cook, stirring often, until most of wine evaporates. Add pasta and beans; toss to combine. Add reserved pasta cooking liquid, a couple of tablespoons at a time, if mixture is too dry. Stir in remaining tomatoes, vinegar, and salt. Divide pasta mixture among 4 bowls. Top evenly with burrata, thyme, and pepper.