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Ensemble Kalman filters are an efficient class of algorithms for large-scale ensemble data assimilation, but their performance is limited by their underlying Gaussian approximation. A two-step framework for ensemble data assimilation allows this approximation to be relaxed: The first step updates the ensemble in observation space, while the second step regresses the observation state update back to the state variables. This paper develops a new quantile-conserving ensemble filter based on kernel-density estimation and quadrature for the scalar first step of the two-step framework. It is shown to perform well in idealized non-Gaussian problems, as well as in an idealized model of assimilating observations of sea-ice concentration.