The actin cortex is a thin cross-linked network attached to the plasma membrane, which is responsible for the cell's shape during migration, division, and growth. In a reductionist approach, we created a minimal actin cortex (MAC) attached to a lipid membrane to correlate the filamentous actin architecture with its viscoelastic properties. The system is composed of a supported 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphocholine bilayer doped with the receptor lipid phosphatidylinositol(4,5)-bisphosphate (PtdIns(4,5)P) to which a constitutively active mutant of ezrin, which is a direct membrane-cytoskeleton linker, is bound. The formation of the MAC on the supported lipid bilayer is analyzed as a function of increasing PtdIns(4,5)P/ezrin pinning points, revealing an increase in the intersections between actin filaments, that is, the node density of the MAC. Bead tracking microrheology on the membrane-attached actin network provides information about its viscoelastic properties. The results show that ezrin serves as a dynamic cross-linker for the actin cortex attached to the lipid bilayer and that the stiffness of the network is influenced by the pinning point density, relating the plateau storage modulus G to the node density of the MAC.