The lack of wide coverage datasets annotated with everyday metaphorical expressions for languages other than English is striking. This means that most research on supervised metaphor detection has been published only for that language. In order to address this issue, this work presents the first corpus annotated with naturally occurring metaphors in Spanish large enough to develop systems to perform metaphor detection. The presented dataset, CoMeta, includes texts from various domains, namely, news, political discourse, Wikipedia and reviews. In order to label CoMeta, we apply the MIPVU method, the guidelines most commonly used to systematically annotate metaphor on real data. We use our newly created dataset to provide competitive baselines by fine-tuning several multilingual and monolingual state-of-the-art large language models. Furthermore, by leveraging the existing VUAM English data in addition to CoMeta, we present the, to the best of our knowledge, first cross-lingual experiments on supervised metaphor detection. Finally, we perform a detailed error analysis that explores the seemingly high transfer of everyday metaphor across these two languages and datasets.