Higgs decay to a pair of charm quarks is a process that has potential to shed light on the standard model Higgs-charm Yukawa coupling and BSM physics in the form of two Higgs doublet models (2HDMs). However, it has not yet been observed experimentally. TThis thesis presents the current status of a search for the titular t$\bar{\text{t}}$H(h$\rightarrow$ c$\bar{\text{c}})$ process. The primary focus in this work is the single-lepton channel, which will utilize the full CMS Run II data set of 138 fb$^{-1}$. This analysis takes advantage of recent advances in machine learning to obtain high jet-tagging and event classification performance, and reports a preliminary new constraint on the t$\bar{\text{t}}$H(h$\rightarrow$ c$\bar{\text{c}})$ cross-section.