Travis M. wrote
What does "brunching" mean?

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Please note that he said "bruching" and not "brunching."

Perhaps he is referring to the practice of core aerating a lawn
and then topdressing with so-called "sharp sand" (ie, course
sand). The topdressing is rake to get as much as possible
down into the aeration cores.

I don't like the term "sharp sand" - I prefer the phrase "course
sand."