Whisk together vinegar, garlic, mustard, mint, 1/4 teaspoon salt, 1/8 teaspoon pepper. Whisk in olive oil.
Combine tomatoes, basil and 3 tablespoons of the dressing. Cover and set aside.
Brush chicken with remaining dressing and season with remaining 1/4 teaspoon of salt and 1/8 teaspoon of pepper. Grill over medium-high heat for 5-6 minutes each side. Scatter cheese over top during last minute of cooking.
Toss coked pasta with tomato salad. Serve with chicken.