  Most searches for top partners, $T$, are concerned with top partner pair
production. However, as these bounds become increasingly stringent, the LHC
energy will saturate and single top partner production will become more
important. In this paper we study the novel signature of the top partner
produced in association with the SM top, $pp\rightarrow
T\overline{t}+t\overline{T}$, in a model where the Standard Model (SM) is
extended by a vector-like $SU(2)_L$ singlet fermion top partner and a real, SM
gauge singlet scalar, $S$. In this model, $pp\rightarrow
T\overline{t}+t\overline{T}$ production is possible through loops mediated by
the scalar singlet. We find that, with reasonable coupling strengths, the
production rate of this channel can dominate top partner pair production at top
partner masses of $m_T\gtrsim 1.5$ TeV. In addition, this model allows for the
exotic decay modes $T\rightarrow tg$, $T\rightarrow t \gamma$, and
$T\rightarrow t S$. In much of the parameter space the loop induced decay
$T\rightarrow tg$ dominates and the top partner is quite long lived. New search
strategies are necessary to cover these decay modes. We project the the
sensitivity of the high luminosity LHC to $pp\rightarrow
T\overline{t}+t\overline{T}$ via a realistic collider study. We find with 3
ab$^{-1}$, the LHC is sensitive to this process for masses $m_T\lesssim2$ TeV.
In addition, we provide appendices detailing the renormalization of this model.
