The objective of the present paper is to develop a rigorous identification methodology of nonlinear normal modes (NNMs) of engineering structures. This is achieved by processing experimental measurements collected under broadband forcing. The use of such a type of forcing signal allows to excite multiple NNMs simultaneously and, in turn, to save testing time. A two-step methodology integrating nonlinear system identification and numerical continuation of periodic solutions is proposed for the extraction of the individual NNMs from broadband input and output data. It is demonstrated using a numerical cantilever beam possessing a cubic nonlinearity at its free end. The proposed methodology can be viewed as a nonlinear generalization of the phase separation techniques routinely utilized for experimental modal analysis of linear structures. The paper ends with a comparison between this new nonlinear phase separation technique and a previously developed nonlinear phase resonance method.