Water-based processing of graphene-typically considered as physicochemically incompatible with water in the macroscale-emerges as the key challenge among the central postulates of green nanotechnology. These problematic concerns are derived from the complex nature of graphene in the family of sp2-carbon nanoallotropes. Indeed, nanomaterials hidden under the common "graphene" signboard are very rich in morphological and physicochemical variants. In this work, inspired by the adhesion chemistry of mussel biomaterials, we have synthesized novel, water-processable graphene-polylevodopa (PDOPA) hybrids. Graphene and PDOPA were covalently amalgamated via the "growth-from" polymerization of l-DOPA (l-3,4-dihydroxyphenylalanine) monomer in air, yielding homogeneously PDOPA-coated (23 wt %) (of thickness 10-20 nm) hydrophilic flakes. The hybrids formed >1 year stable and water-processable aqueous dispersions and further conveniently processable paints of viscosity 0.4 Pa·s at 20 s-1 and a low yield stress τ0 up to 0.12 Pa, hence exhibiting long shelf-life stability and lacking sagging after application. Demonstrating their applicability, we have found them as surfactant-like nanoparticles stabilizing the larger, pristine graphene agglomerates in water in the optimized graphene/graphene-PDOPA weight ratio of 9:1. These characteristics enabled the manufacture of conveniently paintable coatings of low surface resistivity of 1.9 kΩ sq-1 (0.21 Ω·m) which, in turn, emerge as potentially applicable in textronics, radar-absorbing materials, or electromagnetic interference shielding.