  In this paper, we study the dimensionally reduced twisted Kapustin-Witten
equations on the product of a compact Riemann surface $\Sigma$ with
$\mathbb{R}^+$. The main result is a Kobayashi-Hitchin type correspondence
between the space of tilted Nahm pole solutions and the moduli space of
Beilinson-Drinfeld opers. This corroborates a prediction of Gaiotto and Witten
\cite[p.971]{gaiotto2012knot}.
