  In this paper, we derive a formula for the p-adic syntomic regulators of
Asai--Flach classes. These are cohomology classes forming an Euler system
associated to a Hilbert modular form over a quadratic field, introduced in an
earlier paper (arXiv:1607.07813) by Antonio Lei and the first and third
authors. The formula we develop here is expressed in terms of differential
operators acting on overconvergent Hilbert modular forms; it is analogous to
existing formulae for the regulators of Beilinson--Flach classes, but a novel
feature is the appearance of a projection operator associated to a
critical-slope Eisenstein series. We conclude the paper with numerical
calculations giving strong evidence for the non-vanishing of these regulators
in an explicit example.
