  It is well-known that type II two Higgs doublet models (2HDMs) can struggle
to facilitate a strong first-order electroweak phase transition in the early
universe whilst remaining theoretically appealing scenarios for many reasons.
We analyse this apparent shortfall from the perspective of additional new
physics. Starting from a consistent dimension-6 effective field theory Higgs
potential extension, we identify the Higgs potential extensions that provide
the necessary additional contributions required to achieve a strong first-order
electroweak phase transition and trace their phenomenological implications for
the Large Hadron Collider. In passing, we critically assess the reliability of
the dimension-6 approximation depending on the expected 2HDM phenomenology. In
particular, we focus on the role of Higgs pair production (resonant and
non-resonant) and interference effects expected in top final states, which are
the prime candidates of 2HDM exotics discoveries.
