Preheat oven to 350 degrees and line a baking sheet with a silpat. If you don't have a silpat, grease the baking sheet with cooking spray.
Combine the cheddar and cornmeal in a bowl and arrange in small piles on the baking sheet about 2 inches in diameter. Place in the oven and bake for about 7 minutes until the edges start to turn golden brown and the centers look lace-like. Remove from oven and let cool 1 minute.
Remove the cheddar crisps from the baking sheet and drape over the back of a muffin tin or a small glass pinching the sides so that it forms into a cup shape. Let cool for 5 minutes to harden.
Combine the tomatoes, onion, basil, olive oil, vinegar, salt and pepper in a small bowl and toss to combine.
Spoon the tomato salad into the cheese cups and serve.