  We construct proper good moduli spaces parametrizing K-polystable
$\mathbb{Q}$-Gorenstein smoothable log Fano pairs $(X, cD)$, where $X$ is a
Fano variety and $D$ is a rational multiple of the anti-canonical divisor. We
then establish a wall-crossing framework of these K-moduli spaces as $c$
varies. The main application in this paper is the case of plane curves of
degree $d \geq 4$ as boundary divisors of $\mathbb{P}^2$. In this case, we show
that when the coefficient $c$ is small, the K-moduli space of these pairs is
isomorphic to the GIT moduli space. We then show that the first wall crossing
of these K-moduli spaces are weighted blow-ups of Kirwan type. We also describe
all wall crossings for degree 4,5,6, and relate the final K-moduli spaces to
Hacking's compactification and the moduli of K3 surfaces.
