After reionization, neutral hydrogen (H1) traces the large-scale structure (LSS) of the Universe, enabling H1 intensity mapping (IM) to capture the LSS in 3D and constrain key cosmological parameters. We present a new framework utilizing higher order. cross-correlations to study H 1 clustering around galaxies, tested using real-space data from the IllustrisTNG300 simulation. This approach computes the joint distributions of k-nearest neighbour (kNN) optical galaxies and the H 1 brightness temperature field smoothed at relevant scales (the KNN-field framework), providing sensitivity to all higher order cross-correlations, unlike two-point statistics. To simulate H I data from actual surveys, we add random thermal noise and apply a simple foreground cleaning model, filtering out Fourier modes of the brightness temperature field with k(
) < k(min
). Under current levels of thermal noise and foreground cleaning, typical of a Canadian Hydrogen Intensity Mapping Experiment (CHIME)-like survey, the H1-galaxy cross-correlation signal in our simulations, using the kNN-field framework, is detectable at 300 across = [3, 12]h(-1) Mpc. In contrast, the detectability of the standard two-point correlation function (2PCF) over the same scales depends strongly on the foreground filter: a sharp k(
) filter can spuriously boost detection to 8 sigma due to position-space ringing, whereas a less sharp filter yields no detection. None the less, we conclude that NN-field cross-correlations are robustly detectable across a broad range of foreground filtering and thermal noise conditions, suggesting their potential for enhanced constraining power over 2PCFs.