1. Preheat the oven to 375°​F. Line a large rimmed baking sheet with aluminum foil. Place the zucchini, squash, eggplant, mushrooms, shallot halves, sherry vinegar, thyme, 1/4 cup of the oil, 1 teaspoon of the salt, and 1/2 teaspoon of the pepper in a large bowl; toss to combine, coating all the vegetables.

2. Spread the vegetables in a single layer on the prepared baking sheet, and bake until the vegetables are caramelized and softened, 45 to 50 minutes. Remove the vegetables from the pan, and cool to room temperature.

3. Meanwhile, whisk together the balsamic vinegar, chopped shallot, honey, mustard, and remaining 1/2 teaspoon salt and 1/4 teaspoon pepper in a small bowl. Let stand for 2 minutes.

4. Add the remaining 5 tablespoons oil in a slow, steady stream, whisking into the balsamic mixture until blended. Toss together the roasted vegetables and cherry tomatoes with half of the dressing.

5. Place the torn romaine in a large bowl or arrange on a large platter. Spoon the vegetable mixture over the lettuce; sprinkle with the feta and basil. Serve the salad with the remaining dressing.