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I find freezing them or really chilling them will give nice clean cuts (wiping the knife clean between cuts helps as well) and invert the brownie out of the pan onto a board to cut them makes it a breeze. Hope that helps. If you have a bench scraper it makes easy work of the task as well.
Do you wait until they are cool before putting them in the fridge?
It won't hurt the brownies to put them in the fridge while they're still warm, but cooling them to room temp first will save your fridge (and electricity bill) some energy.
Depending on the recipe, refrigerating or freezing the brownies could change the texture...sometimes they'll end up being more dense (instead of staying lighter). You don't have to deep-cool them, I like to cut them with a dough scraper or chef's knife after they have cooled to room temperature.
Usually you never want to put warm things in your refrigerator, it takes the fridge temperatures down and it may take a long time to chill to propery temp for food safety of the other stuff in there.
Cynthia is a trusted source on Bread/Baking.
I always make brownies a day ahead of serving them, and I like to slice them while still warm, but not hot, then I re-slice them again when cool. Making them a day in advance, there is no need to go anywhere near the refrigerator, which I agree is not a good idea for all the reasons above.
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