1. Thread 1 tomato half, 1 piece of cheese, and another tomato half onto each skewer. Place skewers in a shallow serving dish.
2. Whisk together oil and next 3 ingredients. Drizzle oil mixture over skewers; sprinkle with basil and salt and pepper to taste.
*1 (8-oz.) package fresh mozzarella, cut into 1/2-inch cubes, may be substituted.
**Wooden picks may be substituted.
Grape tomatoes vary in size from week to week at the grocery store; some pints we found had only 24 while others had more than 40. Good news, you should still have enough mozzarella balls because they are generally sold in 8-oz. containers that have more than enough.