The periodic Anderson model}, traditionally realized in rare-earth compounds with limited tunability, have hindered systematic exploration of correlated quantum phenomena. Here, we introduce a strategy for realizing and engineering this model in incommensurate van der Waals heterostructures by coupling a Mott insulator (Nb₃Cl₈) with itinerant electrons (from monolayer graphene), circumventing strict lattice-matching requirements. Through magnetotransport and slave spin mean-field calculations, we demonstrate the hybridization gap (Δ≈30 meV), gate-tunable metal-insulator transition, and band-selective electron effective mass enhancement, hallmarks of Kondo coherence. The heterostructure exhibits a nearly order-of-magnitude enhancement in the effective electron mass between hybridized and conventional graphene-like regimes, alongside in-plane magnetic field-induced metal-insulator transitions. Top gate-temperature phase mapping reveals competing correlated states, including insulating and hidden-order phases. This work establishes an electrically tunable van der Waals platform for studying correlated states generated by coupling a Mott-insulating layer to an itinerant-electron system, providing a materials route for exploring low-dimensional correlated quantum phases.