Significant uncertainties related to the choice of the top-quark mass renormalisation scheme are present in the leading and next-to-leading order QCD predictions for di-Higgs production amplitude at hadron colliders. In this talk, I will focus on exploring the origin of these sizeable logarithmic mass corrections in the $gg \to HH$ amplitude at leading and next-to-leading power in the high-energy limit using the Method of Regions and Soft-Collinear Effective Theory. I will present leading power leading-logarithmic resummation results, discuss subleading logarithmic contributions, and show the phenomenological impact of our analysis on the double Higgs production amplitude at high energy.