  Let $K$ be an imaginary quadratic field, with associated quadratic character
$\alpha$. We construct an analytic $p$-adic $L$-function interpolating the
twisted adjoint $L$-values $L(1, \mathrm{ad}(f) \otimes \alpha)$ as $f$ varies
in a Hida family; these special values are non-critical in the sense of
Deligne. Our approach is based on Greenberg--Stevens' idea of $\Lambda$-adic
modular symbols, which considers cohomology with values in a space of $p$-adic
measures.
