Thanks to very deep spectroscopic observations carried out at the Large Binocular Telescope, we measured simultaneously stellar age, metallicity and velocity dispersion for C1-23152, an ETG at redshift $z$=3.352, corresponding to an epoch when the Universe was $sim$1.8 Gyr old. The analysis of its spectrum shows that this galaxy, hosting an AGN, formed and assembled $sim$2$times$10$^{11}$ M$_odot$ shaping its morphology within the $sim$600 Myr preceding the observations, since $z$$sim$4.6. The stellar population has a mean mass-weighted age 400$^{+30}_{-70}$ Myr and it is formed between $sim$600 Myr and $sim$150 Myr before the observed epoch, this latter being the time since quenching. Its high stellar velocity dispersion, $sigma_e$=409$pm$60 km s$^{-1}$, confirms the high mass (M$_{dyn}$=$2.2(pm0.4)$$times$10$^{11}$ M$_odot$) and the high mass density ($Sigma_e^{M^*}$=$Sigma_{1kpc}=3.2(pm0.7)times10^{10}$ M$_odot$ kpc$^{-2}$), suggesting a fast dissipative process at its origin. The analysis points toward a supersolar metallicity, [Z/H]=0.25$^{+0.006}_{-0.10}$, in agreement with the above picture, suggesting a star formation efficiency much higher than the replenishment time. However, sub-solar metallicity values cannot be firmly ruled out by our analysis. Quenching must have been extremely efficient to reduce the star formation to SFR$<$6.5 M$_odot$ yr$^{-1}$ in less than 150 Myr. This could be explained by the presence of the AGN, even if a causal relation cannot be established from the data. C1-23152 has the same stellar and physical properties of the densest ETGs in the local Universe of comparable mass, suggesting that they are C1-23152-like galaxies which evolved to $z=0$ unperturbed.
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