Speech-based analysis offers a scalable and non-invasive approach for detecting cognitive decline, yet progress has been constrained by the limited availability of clinically validated datasets collected under realistic conditions. We introduce PROCESS-2, a large-scale speech dataset designed to support research on automatic assessment of cognitive impairment from spontaneous and task-oriented speech. The dataset comprises recordings from 200 healthy controls, 150 mild cognitive impairment, and 50 dementia diagnoses collected using the CognoMemory digital assessment platform. Each participant completed a single assessment session, including picture description and verbal fluency tasks, accompanied by manually verified transcripts and participant-level metadata. PROCESS-2 contains approximately 21 hours of speech audio with predefined train/test partitions. Comprehensive technical validation evaluated demographic balance, clinical consistency, recording stability, embedding-space structure, and reproducible baseline modelling performance, demonstrating clinically meaningful group separation and stable performance across modelling approaches while preserving real-world conversational variability. PROCESS-2 is released under controlled access via Hugging Face to enable responsible reuse while protecting participant privacy, providing a reproducible benchmark resource for speech-based cognitive assessment research.