Cloud systems are large scalable distributed systems that must be carefully monitored to timely detect problems and anomalies. While a number of cloud monitoring frameworks are available, only a few solutions address the problem of adaptively and dynamically selecting the indicators that must be collected, based on the actual needs of the operator. Unfortunately, these solutions are either limited to infrastructure-level indicators or technology-specific, for instance, they are designed to work with OpenStack but not with other cloud platforms. This paper presents the VARYS monitoring framework, a technology-agnostic Monitoring-as-a-Service solution that can address KPI monitoring at all levels of the Cloud stack, including the application-level. Operators use VARYS to indicate their monitoring goals declaratively, letting the framework to perform all the operations necessary to achieve a requested monitoring configuration automatically. Interestingly, the VARYS architecture is general and extendable, and can thus be used to support increasingly more platforms and probing technologies.