We say that a metric g in a torus cusp is asymptotically cusped if there exists a hyperbolic cusped metric so that its difference with g converges to 0 in C^1 as we go along the cusp. In this talk we will describe minimal surface entropy for asymptotically cusped metrics, which is a geometric invariant established by Calegari-Marques-Neves and defined as the asymptotic counting of compact minimal surfaces as area grows. We will show an entropy rigidity for finite volume hyperbolic 3-manifolds. Namely, if M is a 3-manifold that admits a cusped hyperbolic metric of finite volume, then the hyperbolic metric can be characterized as the metric minimizing minimal surface entropy among negatively curved, asymptotically cusped metrics. This is based on upcoming joint work with Ruojing Jiang.