Using the data from the Sloan Digital Sky Survey and the Gaia satellite, we assemble a pure sample of ~3000 blue horizontal branch (BHB) stars with 7D information, including positions, velocities, and metallicities. We demonstrate that, as traced with BHBs, the Milky Way's stellar halo is largely unmixed and cannot be well represented with a conventional Gaussian velocity distribution. A single-component model fails because the inner portions of the halo are swamped with metal-rich tidal debris from an ancient, head-on collision, known as the 'Gaia Sausage'. Motivated by the data, we build a flexible mixture model that allows us to track the evolution of the halo make-up across a wide range of radii. It is built from two components, one representing the radially anisotropic Sausage stars with their lobed velocity distribution, and the other representing a more metal-poor and more isotropic component built up from minor mergers. We show that inside 25kpc the 'Sausage' contributes at least 50 per cent of the Galactic halo. The fraction of 'Sausage' stars diminishes sharply beyond 30kpc, which is the long-established break radius of the classical stellar halo.