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Strongly interacting electrons in layered materials give rise to a plethora of emergent phenomena, such as unconventional superconductivity. heavy fermions, and spin textures with non-trivial topology. Similar effects can also be observed in bulk materials, but the advantage of two dimensional (2D) systems is the combination of local accessibility by microscopic techniques and tuneability. In stacks of 2D materials, for example, the twist angle can be employed to tune their properties. However, while material choice and twist angle are global parameters, the full complexity and potential of such correlated 2D electronic lattices will only reveal itself when tuning their parameters becomes possible on the level of individual lattice sites. Here, we discover a lattice of strongly correlated electrons in a perfectly ordered 2D supramolecular network by driving this system through a cascade of quantum phase transitions using a movable atomically sharp electrostatic gate. As the gate field is increased, the molecular building blocks change from a Kondo-screened to a paramagnetic phase one-by-one, enabling us to reconstruct their complex interactions in detail. We anticipate that the supramolecular nature of the system will in future allow to engineer quantum correlations in arbitrary patterned structures.