  To study the quantized Coulomb branch of 3d $\mathcal{N}=4$ unitary SQCD
theories, we propose a new method to compute correlators of monopole and
Casimir operators that are inserted in the
$\mathbb{R}\times\mathbb{R}^2_\epsilon$ Omega background. This method combines
results from supersymmetric localization with inputs from the brane realisation
of the correlators in type IIB string theory. The main challenge is the
computation of the partition functions of certain Super-Matrix-Models (SMMs),
which appear in the contribution of monopole bubbling sectors and are realised
as the theory living on the D1 strings in the brane construction. We find that
the non-commutativity arising in the monopole operator insertions is related to
a wall-crossing phenomenon in the FI parameter space of the SMM. We illustrate
our method in various examples and we provide explicit results for arbitrary
correlators of non-bubbling bare monopole operators. We also discuss the
realisation of the non-commutative product as a Moyal (star) product and use it
to successfully test our results.
