Despite his boss browbeating him to work overtime, he insisted on leaving on time.

browbeating 是动词 browbeat 的现在分词形式。browbeat 由 brow（眉毛）和 beat（击打）组成，字面意思是"用眉毛击打"，引申为"用严厉的表情或言语威吓、胁迫"。browbeating 在这里表示"持续不断地威吓"的动作。