Preheat grill to a medium-high heat. Brush shucked corn with a small amount of vegetable or canola oil and grill over medium-high heat, turning as needed, until slightly charred (10-15 minutes). Set aside to cool.
In a small bowl, combine minced shallot and white wine vinegar; let sit for 5 minutes. Whisk in olive oil and salt and pepper to taste. When corn has cooled, slice kernels off cobs and place them in a large bowl. Add raw zucchini, cherry tomatoes, cheese, scallions, and dressing; toss to coat. Add basil and stir in gently, then serve warm or at room temperature.