  Radio transient searches using traditional variability metrics struggle to
recover sources whose evolution timescale is significantly longer than the
survey cadence. Motivated by the recent observations of slowly evolving radio
afterglows at gigahertz frequency, we present the results of a search for radio
variables and transients using an alternative matched-filter approach. We
designed our matched-filter to recover sources with radio light curves that
have a high-significance fit to power-law and smoothly broken power-law
functions; light curves following these functions are characteristic of
synchrotron transients, including "orphan" gamma-ray burst afterglows, which
were the primary targets of our search. Applying this matched-filter approach
to data from Variables and Slow Transients Pilot Survey conducted using the
Australian SKA Pathfinder, we produced five candidates in our search.
Subsequent Australia Telescope Compact Array observations and analysis revealed
that: one is likely a synchrotron transient; one is likely a flaring active
galactic nucleus, exhibiting a flat-to-steep spectral transition over
$4\,$months; one is associated with a starburst galaxy, with the radio emission
originating from either star formation or an underlying slowly evolving
transient; and the remaining two are likely extrinsic variables caused by
interstellar scintillation. The synchrotron transient, VAST J175036.1$-$181454,
has a multi-frequency light curve, peak spectral luminosity, and volumetric
rate that is consistent with both an off-axis afterglow and an off-axis tidal
disruption event; interpreted as an off-axis afterglow would imply an average
inverse beaming factor $\langle f^{-1}_{\text{b}} \rangle =
860^{+1980}_{-710}$, or equivalently, an average jet opening angle of $\langle
\theta_{\textrm{j}} \rangle = 3^{+4}_{-1}\,$deg.
