Following the increasing interest and adoption of FaaS systems, benchmarking frameworks for determining nonfunctional properties have also emerged. While existing (microbenchmark) frameworks only evaluate single aspects of FaaS platforms, a more holistic, application-driven approach is still missing. In this paper, we design and present BeFaaS, an extensible application-centric benchmarking framework for FaaS environments that focuses on the evaluation of FaaS platforms through realistic and typical examples of FaaS applications. BeFaaS includes a built-in e-commerce benchmark, is extensible for new workload profiles and new platforms, supports federated benchmark runs in which the benchmark application is distributed over multiple providers, and supports a fine-grained result analysis. Our evaluation compares three major FaaS providers in single cloud provider setups and shows that BeFaaS is capable of running each benchmark automatically with minimal configuration effort and providing detailed insights for each interaction.