Butter a 13x9x2 glass baking dish.
In a medium mixing bowl, whisk together the eggs, milk, salt and freshly ground black pepper.
Arrange the bread cubes in the bottom of the prepared baking dish, then scatter the tomatoes, cheese and chopped herbs on top.
Pour the milk and egg mixture over top of the breads, pressing down to submerge everything completely. Cover the dish with plastic wrap and place it in the refrigerator for at least a few hours -- preferably overnight -- to allow the breads to soak up all the milk.
To bake, position a rack in the center of the oven and preheat to 350 F.
Bake the strata uncovered until puffed and golden, and a knife inserted into its center comes out clean, about 1 hour. Let stand for 10 minutes. Cut the strata into squares and serve.