Real-world tasks often lack large labeled datasets, motivating extensive work on learning in low-data regimes. However, existing approaches such as few-shot prompting, instruction tuning, and synthetic data generation, continue to treat labeled or pseudo-labeled data as the primary learning signal. In contrast, human practitioners acquire expertise through repeated, self-directed interaction with the open web, progressively refining both domain knowledge and search strategies. We propose MEMENTO, a framework that treats the web as a learning signal rather than a stateless retrieval interface. MEMENTO operates at two levels: within each session, it conducts iterative web exploration via an Adaptive Exploration Tree (AET) that decomposes tasks into evolving questions and reflects on intermediate findings; across sessions, it accumulates experience through dual-channel memory, separating declarative knowledge (facts) from procedural knowledge (search strategies). This design enables agents to learn reusable research strategies and domain expertise from trajectories of web interaction without additional model training. We evaluate MEMENTO on two low-data professional domains: sales automation and legal research. Our empirical results show consistent improvements in performance over ReAct based baselines (+25.6% on sales automation and 36.5% on legal research), demonstrating that the web can serve as a scalable learning source for acquiring task-specific expertise in data-scarce settings.