In neutral graphene, two prominent cusps known as Kohn anomalies are found in the phonon dispersion of the highest optical phonon at q=Γ (LO branch) and q=K (TO branch), reflecting a significant electron-phonon coupling (EPC) to undoped Dirac electrons. In this work, high-resolution electron energy loss spectroscopy is used to measure the phonon dispersion around the Γ point in quasifreestanding graphene epitaxially grown on Pt(111). The Kohn anomaly for the LO phonon is observed at finite momentum q~2k_{F} from Γ, with a shape in excellent agreement with the theory and consistent with known values of the EPC and the Fermi level. More strikingly, we also observe a Kohn anomaly at the same momentum for the out-of-plane optical phonon (ZO) branch. This observation is the first direct evidence of the coupling of the ZO mode with Dirac electrons, which is forbidden for freestanding graphene but becomes allowed in the presence of a substrate. Moreover, we estimate the EPC to be even greater than that of the LO mode, making graphene on Pt(111) an optimal system to explore the effects of this new coupling in the electronic properties.