Today's online platforms rely heavily on recommendation systems to serve content to their users; social media is a prime example. In turn, recommendation systems largely depend on artificial intelligence algorithms to decide who gets to see what. While the content social media platforms deliver is as varied as the users who engage with them, it has been shown that platforms can contribute to serious harm to individuals, groups and societies. Studies have suggested that these negative impacts range from worsening an individual's mental health to driving society-wide polarisation capable of putting democracies at risk. To better safeguard people from these harms, the European Union's Digital Services Act (DSA) requires platforms, especially those with large numbers of users, to make their algorithmic systems more transparent and follow due diligence obligations. These requirements constitute an important legislative step towards mitigating the systemic risks posed by online platforms. However, the DSA lacks concrete guidelines to operationalise a viable audit process that would allow auditors to hold these platforms accountable. This void could foster the spread of 'audit-washing', that is, platforms exploiting audits to legitimise their practices and neglect responsibility. To fill this gap, we propose a risk-scenario-based audit process. We explain in detail what audits and assessments of recommender systems according to the DSA should look like. Our approach also considers the evolving nature of platforms and emphasises the observability of their recommender systems' components. The resulting audit facilitates internal (among audits of the same system at different moments in time) and external comparability (among audits of different platforms) while also affording the evaluation of mitigation measures implemented by the platforms themselves.