Broodingly is an adverb used to describe someone's thoughtfulness, deep thinking or intently focused mental state. Here are some synonyms that may help you to diversify your vocabulary: contemplatively, meditatively, pensively, reflectively, introspectively, ruminatively, thoughtfully, raptly, concentratedly, intensely, absorbedly, self-absorbedly, studiously, attentively, musingly. These words all convey a similar meaning to broodingly, but each one adds a slightly different connotation that may better suit your context. If you use synonyms effectively, it can provide your writing with more depth and vividness. However, it's important to choose the right synonym that fits your intended meaning.