Brownies generally have a lower ratio of flour to fat (butter and eggs) than many other baked goods, which makes them more prone to caving in the center. When you beat the eggs and butter you incorporate air into them, and the flour stabilizes the air bubbles. But if too much air is in the mixture for the amount of flour, the brownies "over-expand" as they bake, but collapse, or cave in, as they cool and the unstable air bubbles deflate.
To avoid this problem, says Michelle Tampakis, Senior Baking Instructor at the Institute of Culinary Education in New York City, (1) add the eggs one at a time, and beat between each addition, and (2) avoid over beating the mixture—meaning too long or at too high a speed. If you need a top-notch brownie recipe, see Our Best Brownies.
Recipe: So Good Brownies