There's no way.
What's happening is the brownies rise when they bake and form a mound in the middle, filled with warm (expansive) air. When the air cools it contracts and the middle sinks. The edges won't sink as much, because (a) they're held to the side of the pan by stickiness, and (b) they've been toasted so they don't contract as much by virtue of being on the outside, and (c) from contact conduction with the sides of the pan (what Ed described). This leaves the top of the outside a little higher than the general level of brownie. That's the "ridge" you mentioned.
You can trim the edges if you like, but they're chewy and wonderful. If you must trim, send them to me.