  We present late-time observations by Swift and XMM-Newton of the tidal
disruption event (TDE) ASASSN-15oi that reveal that the source brightened in
the X-rays by a factor of $\sim10$ one year after its discovery, while it faded
in the UV/optical by a factor of $\sim 100$. The XMM-Newton observations
measure a soft X-ray blackbody component with $kT_{\rm bb} \sim 45$ eV,
corresponding to radiation from several gravitational radii of a central $\sim
10^6 M_\odot$ black hole. The last Swift epoch taken almost 600 days after
discovery shows that the X-ray source has faded back to its levels during the
UV/optical peak. The timescale of the X-ray brightening suggests that the X-ray
emission could be coming from delayed accretion through a newly forming debris
disk, and that the prompt UV/optical emission is from the prior circularization
of the disk through stream-stream collisions. The lack of spectral evolution
during the X-ray brightening disfavors ionization breakout of a TDE "veiled" by
obscuring material. This is the first time a TDE has been shown to have a
delayed peak in soft X-rays relative to the UV/optical peak, which may be the
first clear signature of the real-time assembly of a nascent accretion disk,
and provides strong evidence for the origin of the UV/optical emission from
circularization, as opposed to reprocessed emission of accretion radiation.
