How do I stop my brownies from rising?
Well, if air is the only raising agent, simply add less of it by not beating the mixture as much. Failing that, beat as normal, then give the mixing bowl a couple of (careful) bangs on the counter top to knock the air out it again.

A bit of experimentation will be necessary to get the right results, I think: perhaps pour some of the mixture into the tin as is, then knock the air out of the remaining mixture and compare the results.