  Let $X = X_\Sigma$ be a toric surface and $(\check{X}, W)$ be its
Landau-Ginzburg (LG) mirror where $W$ is the Hori-Vafa potential. We apply
asymptotic analysis to study the extended deformation theory of the LG model
$(\check{X}, W)$, and prove that semi-classical limits of Fourier modes of a
specific class of Maurer-Cartan solutions naturally give rise to tropical disks
in $X$ with Maslov index 0 or 2, the latter of which produces a universal
unfolding of $W$. For $X = \mathbb{P}^2$, our construction reproduces Gross'
perturbed potential $W_n$ which was proven to be the universal unfolding of $W$
written in canonical coordinates. We also explain how the extended deformation
theory can be used to reinterpret the jumping phenomenon of $W_n$ across walls
of the scattering diagram formed by the Maslov index 0 tropical disks
originally observed by Gross (in the case of $X = \mathbb{P}^2$).
