The persisting threats on migratory bird populations highlight the urgent need for effective monitoring techniques that could assist in their conservation. Among these, passive acoustic monitoring is an essential tool, particularly for nocturnal migratory species that are difficult to track otherwise. This work presents the Nocturnal Bird Migration (NBM) dataset, a collection of 13,359 annotated vocalizations from 117 species of the Western Palearctic. The dataset includes precise time and frequency annotations, gathered by dozens of bird enthusiasts across France, enabling novel downstream acoustic analysis. In particular, we prove the utility of this database by training an original two-stage deep object detection model tailored for the processing of audio data. While allowing the precise localization of bird calls in spectrograms, this model shows competitive accuracy on the 45 main species of the dataset with state-of-the-art systems trained on much larger audio collections. These results highlight the interest of fostering similar open-science initiatives to acquire costly but valuable fine-grained annotations of audio files. All data and code are made openly available.