In this work, we propose a novel framework for privacy-preserving client-distributed machine learning. It is motivated by the desire to achieve differential privacy guarantees in the local model of privacy in a way that satisfies all systems constraints using asynchronous client-server communication and provides attractive model learning properties. We call it "Draw and Discard" because it relies on random sampling of models for load distribution (scalability), which also provides additional server-side privacy protections and improved model quality through averaging. We present the mechanics of client and server components of "Draw and Discard" and demonstrate how the framework can be applied to learning Generalized Linear models. We then analyze the privacy guarantees provided by our approach against several types of adversaries and showcase experimental results that provide evidence for the framework's viability in practical deployments.