We focus on the problem of parsing procedural text into fine-grained flow graphs that encode actions and entities, as well as their interactions. Specifically, we focus on parsing cooking recipes, and address a few limitations of existing parsers. Unlike SOTA approaches to flow graph parsing that work in two separate stages identifying actions and entities (tagging) and encoding their interactions via connecting edges (graph generation). we propose an end-to-end multi-task framework that simultaneously performs tagging and graph generation. In addition, due to the end-to-end nature of our proposed model, we can unify the input representation, and moreover can use compact encoders, resulting in small models with significantly fewer parameters than SOTA models. Another key challenge in training flow graph parsers is the lack of sufficient annotated data, due to the costly nature of the fine-grained annotations. We address this problem by taking advantage of the abundant unlabelled recipes, and show that pre-training on automatically-generated noisy silver annotations (from unlabelled recipes) results in a large improvement in flow graph parsing.