present evidence for the development of massive bulges within star-forming Main Sequence (SFMS) galaxies at redshift z~2 using the combination of rest-frame Far-UV-to-optical HST imaging and SINFONI Adaptive-Optics spectra of the Halpha line emission in these systems. Specifically I correct the Halpha and UV star-formation rate (SFR) density maps using dust attenuation maps resolved on scales of a kpc, and derive how, locally on such small scales, the stellar mass density relates to the dust-corrected SFR density. Through this comparison I demonstrate not only that massive SFMS galaxies at the peak of cosmic star-formation activity have already achieved the stellar density distributions that we see in massive spheroids at z=0, but also that they have outward-increasing specific SFR radial profiles, i.e. suppressed star-formation activity in their central bulge regions. These centrally-suppressed star-formation activity is not an artifact of dust obscuration; rather, they indicate that star-forming massive galaxies at z~2 have already started quenching from their inner cores, and will achieve ‘terminal quiescence’ over their whole bodies on timescales of order 1 Gyr. I compare the observed SFR and stellar mass distributions to predictions of state-of-the-art cosmological hydrodynamical zoom-in simulations in order to explore which physical processes can explain our observational results. I will present evidence from the simulations that gas-driven compaction is a key phase in the life of galaxies.