While fewer in number than the dominant rotation-powered radio pulsar population, peculiar classes of isolated neutron stars (INSs) -which include magnetars, the ROSAT-discovered "Magnificent Seven" (M7), rotating radio transients (RRATs), and central compact objects in supernova remnants (CCOs) -represent a key element in understanding the neutron star phenomenology. We report the results of an observational campaign to study the properties of the source 2XMM J104608.7-594306, a newly discovered thermally emitting INS. The evolutionary state of the neutron star is investigated by means of deep dedicated observations obtained with the XMM-Newton Observatory, the ESO Very Large Telescope, as well as publicly available γ-ray data from the Fermi Space Telescope and the AGILE Mission. The observations confirm previous expectations and reveal a unique type of object. The source, which is likely within the Carina Nebula (N H = 2.6 × 10 21 cm −2 ), has a spectrum that is both thermal and soft, with kT ∞ = 135 eV. Non-thermal (magnetospheric) emission is not detected down to 1% (3σ, 0.1-12 keV) of the source luminosity. Significant deviations (absorption features) from a simple blackbody model are identified in the spectrum of the source around energies 0.6 keV and 1.35 keV. While the former deviation is likely related to a local oxygen overabundance in the Carina Nebula, the latter can only be accounted for by an additional spectral component, which is modelled as a Gaussian line in absorption with EW = 91 eV and σ = 0.14 keV (1σ). Furthermore, the optical counterpart is fainter than m V = 27 (2σ) and no γ-ray emission is significantly detected by either the Fermi or AGILE missions. Very interestingly, while these characteristics are remarkably similar to those of the M7 or the only RRAT so far detected in X-rays, which all have spin periods of a few seconds, we found intriguing evidence of very rapid rotation, P = 18.6 ms, at the 4σ confidence level. We interpret these new results in the light of the observed properties of the currently known neutron star population, in particular those of standard rotation-powered pulsars, recycled objects, and CCOs. We find that none of these scenarios can satisfactorily explain the collective properties of 2XMM J104608.7-594306, although it may be related to the still poorly known class of Galactic anti-magnetars. Future XMM-Newton data, granted for the next cycle of observations (AO11), will help us to improve our current observational interpretation of the source, enabling us to significantly constrain the rate of pulsar spin down.