Word Sense Disambiguation (WSD) is a historical NLP task aimed at linking words in contexts to discrete sense inventories and it is usually cast as a multi-label classification task. Recently, several neural approaches have employed sense definitions to better represent word meanings. Yet, these approaches do not observe the input sentence and the sense definition candidates all at once, thus potentially reducing the model performance and generalization power. We cope with this issue by reframing WSD as a span extraction problem --- which we called Extractive Sense Comprehension (ESC) --- and propose ESCHER, a transformer-based neural architecture for this new formulation. By means of an extensive array of experiments, we show that ESC unleashes the full potential of our model, leading it to outdo all of its competitors and to set a new state of the art on the English WSD task. In the few-shot scenario, ESCHER proves to exploit training data efficiently, attaining the same performance as its closest competitor while relying on almost three times fewer annotations. Furthermore, ESCHER can nimbly combine data annotated with senses from different lexical resources, achieving performances that were previously out of everyone's reach. The model along with data is available at https://github.com/SapienzaNLP/esc.