Preheat a cast iron skillet over medium-high heat. Place whole corn cobs into the heated pan, then cook, turning the cobs regularly with tongs, until patches of the kernels turn deeply charred and blackened on the outside. This whole process takes roughly 3 minutes. Set the cooked corn aside to cool, then slice all the kernels off the cob once it is cool enough to handle safely.
Add your prepared corn kernels, cherry tomatoes, fresh basil, and mozzarella to a large shallow serving bowl. To make the vinaigrette, pour vinegar into a separate small bowl, then whisk in mustard, salt, black pepper, minced shallot, and chopped parsley until everything is evenly mixed. Keep whisking vigorously as you slowly stream in the oil to form a smooth, emulsified dressing. Spoon the finished dressing over the salad one tablespoon at a time, stopping once the salad is dressed to your personal taste. Store any leftover dressing in the refrigerator to reuse for other dishes.