From burro +‎ brush.

burrobrush (usually uncountable, plural burrobrushes)

1. An allergenic perennial shrub of species Hymenoclea salsola, found in the deserts of Arizona and neighboring states.

   Synonym: cheesebush

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  Hymenoclea salsola on Wikipedia.Wikipedia
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  Hymenoclea (Asteraceae) on Wikispecies.Wikispecies
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  Category:Hymenoclea salsola on Wikimedia Commons.Wikimedia Commons
• burrobrush at USDA Plants database