We present a new approach for searching for new physics which bridges the gap between on-shell searches and effective field theories. Unlike the traditional Top EFT approach that focus on momentum distribution tails, we explore new physics effects emerging at loop-level, which can manifest as distinct structures on distributions at intermediate energy scales. We illustrate this with a UV model featuring a $\mathcal{Z}_2$ symmetry, incorporating a Dark Matter candidate and a top-partner. Considering the constraints from searches for the on-shell production of the top partner and from 1-loop effects to the top pair production, we illustrate the complementarity of both types of searches. We also compare the 1-loop
results to the ones obtained using the EFT approximation and quantify how much it fails to capture the off-shell effects if the new physics scale is at a few TeV or below.