in a brown study in a reverie; absorbed in your thoughts.

☞ The earliest meaning of brown in English was simply 'dark'. From this, an extended sense of 'gloomy or serious' developed and it is apparently from this sense that we get the phrase in a brown study.

2001New York Review of Books When he isn't stirring up mischief, or conniving for gold, or composing beautiful poetry, he's apt to be sunk in a brown study.