A maker or seller of brooms, or a person of low social status associated with broom-making.
From broom + squire (from Old French 'esquire', originally a young nobleman or attendant, later any gentleman). The term became somewhat derisive for a common tradesman.
This word shows how titles like 'squire' were attached to craftspeople's specialties—broomsquire, scissors-smith, etc.—turning their trade into a quasi-title, which was how medieval people identified themselves before modern surnames.
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