  We give a new proof of Howard's $\Lambda$-adic Gross-Zagier formula, which we
extend to the context of indefinite Shimura curves over $\mathbf{Q}$ attached
to nonsplit quaternion algebras. This formula relates the cyclotomic derivative
of a two-variable $p$-adic $L$-function restricted to the anticyclotomic line
to the cyclotomic $p$-adic heights of Heegner points over the anticyclotomic
tower, and our proof, rather than inspired by the original approaches of
Gross-Zagier and Perrin-Riou, is via Iwasawa theory, based on the connection
between Heegner points, Beilinson-Flach elements, and their explicit
reciprocity laws.
