Podcasting is an increasingly popular medium for entertainment and discourse around the world, with tens of thousands of new podcasts released on a monthly basis. We consider the problem of identifying from these newly-released podcasts those with the largest potential audiences so they can be considered for personalized recommendation to users. We first study and then discard a supervised approach due to the inadequacy of either content or consumption features for this task, and instead propose a novel non-contextual bandit algorithm in the fixed-budget infinitely-armed pure-exploration setting. We demonstrate that our algorithm is well-suited to the best-arm identification task for a broad class of arm reservoir distributions, out-competing a large number of state-of-the-art algorithms. We then apply the algorithm to identifying podcasts with broad appeal in a simulated study, and show that it efficiently sorts podcasts into groups by increasing appeal while avoiding the popularity bias inherent in supervised approaches.