When your brownies are still warm, lightly score them. When cool enough to cut, use a pizza roller/cutter to cut through them. It will cut right through the nuts, if you added them.
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Use a disposable plastic knife as opposed to a regular kitchen knife when cutting brownies. This will cut the brownies cleanly, instead of pulling the brownies and causing an ugly, messy, crumby build up around the edges of each piece.
A warm knife cuts baked items like brownies better than a cold knife. Just run the knife under hot water and then wipe it dry before cutting.