jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pWe study collisions of boosted rotating black holes in jats:italicD</jats:italic> = 6 and 7 spacetime dimensions with a non-zero impact parameter. We find that there exists an open set of initial conditions such that the intermediate state of the collision is a black hole with a dumbbell-like horizon which is unstable to a local Gregory-Laflamme-type instability. We are able to provide convincing numerical evidence that the evolution of such an instability leads to a pinch off of the horizon in finite asymptotic time thus forming a naked singularity, as in similar unstable black holes. Since the black holes in the initial state are stable, this is the first genuinely generic evidence for the violation of the Weak Cosmic Censorship Conjecture in higher dimensional asymptotically flat spacetimes.</jats:p>