Gravitational waves from phase transitions in the early universe are one of our most promising signal channels of BSM physics; however, existing methods for predicting these signals are limited to weakly-coupled theories. In this talk, I present a new, nonperturbative formalism for false vacuum decay that integrates over local fluctuations in field space using the functional renormalization group. As I demonstrate for a simple model, this method opens the door to reliable calculation of gravitational wave signals and false vacuum decay rates for strongly-interacting theories.