  Recently, a new axiomatic framework for tameness in henselian valued fields
was developed by Cluckers, Halupczok, Rideau-Kikuchi and Vermeulen and termed
Hensel minimality. In this article we develop Diophantine applications of
Hensel minimality. We prove a Pila--Wilkie type theorem for transcendental
curves definable in Hensel minimal structures. In order to do so, we introduce
a new notion of point counting in this context related to dimension counting
over the residue field. We examine multiple classes of examples, showcasing the
need for this new dimension counting and prove that our bounds are optimal.
