  Nonlinear extensions of classical Maxwell's electromagnetism are among the
prominent candidates for theories admitting regular black hole solutions. A
quest for such examples has been fruitful, but mostly unsystematic and littered
by the introduction of physically unrealistic Lagrangians. We provide a
procedure which admits the reconstruction of a nonlinear electromagnetic
Lagrangian, consistent with the Euler--Heisenberg Lagrangian in the weak-field
limit, from a given metric representing a regular, magnetically charged black
hole.
