Recent significant improvements in speech and language technologies come both from self-supervised approaches over raw language data as well as various types of explicit supervision. To ensure high-quality processing of spoken data, the most useful type of explicit supervision is still the alignment between the speech signal and its corresponding text transcript, which is a data type that is not available for many languages. In this paper, we present our approach to building large and open speech-and-text-aligned datasets of less-resourced languages based on transcripts of parliamentary proceedings and their recordings. Our starting point are the ParlaMint comparable corpora of transcripts of parliamentary proceedings of 26 national European parliaments. In the pilot run on expanding the ParlaMint corpora with aligned publicly available recordings, we focus on three Slavic languages, namely Croatian, Polish, and Serbian. The main challenge of our approach is the lack of any global alignment between the ParlaMint texts and the available recordings, as well as the sometimes varying data order in each of the modalities, which requires a novel approach in aligning long sequences of text and audio in a large search space. The results of this pilot run are three high-quality datasets that span more than 5,000 hours of speech and accompanying text transcripts. Although these datasets already make a huge difference in the availability of spoken and textual data for the three languages, we want to emphasize the potential of the presented approach in building similar datasets for many more languages.