Livestreaming is now a popular way for programmers, artists, and gamers to teach their craft online. In this paper we propose the idea that streaming can enable cognitive apprenticeship, a form of teaching where an expert works on authentic tasks while thinking aloud to explain their creative process. To understand how streamers teach in this naturalistic way, we performed a content analysis of 20 stream videos across four popular categories: web development, data science, digital art, and gaming. We discovered four kinds of serendipitous teachable moments that are reminiscent of cognitive apprenticeship: 1) creators encountered unexpected errors that led to improvised problem solving, 2) they generated improvised examples on-the-fly, 3) they sometimes went on insightful tangents, 4) they paused to give high-level advice that was contextualized within the work they were currently performing. We also found missed opportunities for additional teachable moments due to creators not being able to express their tacit (unspoken) expert knowledge because of pattern irreducibility, context dependence, and routinization. To better support livestreaming as cognitive apprenticeship, we use our study findings to propose the design of new tools for eliciting tacit knowledge and for repurposing longform streams into shorter, more targeted videos to ease viewer consumption.