The reconstruction of the Higgs potential in the Minimal Supersymmetric Standard Model (MSSM) requires the measurement of the trilinear Higgs self-couplings. The `double Higgs production' subgroup has been investigating the possibility of detecting signatures of processes carrying a dependence on these vertices at the Large Hadron Collider (LHC) and future Linear Colliders (LCs). As reference reactions, we have chosen $gg\to hh$ and $e^+e^-\to h h Z$, respectively, where $h$ is the lightest of the MSSM Higgs bosons. In both cases, the $Hhh$ interaction is involved. For $m_H>2m_h$, the two reactions are resonant in the $H\to hh$ mode, providing cross sections which are detectable at both accelerators and strongly sensitive to the strength of the trilinear coupling involved. We explore this mass regime of the MSSM in the $h\to b\bar b$ decay channel, also accounting for irreducible background effects.