Preheat the broiler.

In a large bowl, beat the eggs with the milk.

Pour 1 tablespoon of the oil into a very large ovenproof skillet, or use 2 skillets with half the ingredients in each. Place over medium heat on the stovetop and pour in the egg mixture. Scatter the tomatoes, cheese, and basil over the eggs. Season with salt and pepper to taste.

When the bottom just begins to brown, place the skillet under the broiler just until the top is set, a minute or less. Remove from the oven and use a large spatula to transfer the frittata to a serving platter. Cool about 10 minutes, cut into wedges, and serve.