  Neutron stars are the dense and highly magnetic relics of supernova
explosions of massive stars. The quest to constrain the Equation of State (EoS)
of ultra-dense matter and thereby probe the behavior of matter inside neutron
stars, is one of the core goals of modern physics and astrophysics. A promising
method involves investigating the long-term cooling of neutron stars, and
comparing theoretical predictions with various sources at different ages.
However, limited observational data, and uncertainties in source ages and
distances, have hindered this approach. In this work, re-analyzing XMM-Newton
and Chandra data from dozens of thermally emitting isolated neutron stars, we
have identified three sources with unexpectedly cold surface temperatures for
their young ages. To investigate these anomalies, we conducted magneto-thermal
simulations across diverse mass and magnetic fields, considering three
different EoS. We found that the "minimal" cooling model, failed to explain the
observations, regardless the mass and the magnetic field, as validated by a
machine learning classification method. The existence of these young cold
neutron stars suggests that any dense matter EoS must be compatible with a fast
cooling process at least in certain mass ranges, eliminating a significant
portion of current EoS options according to recent meta-modelling analysis.
