We introduce a 1+1-dimensional temperature-dependent model such that the classical ballistic deposition model is recovered as its zero-temperature limit. Its & INFIN;-temperature version, which we refer to as the 0-Ballistic Deposition (0-BD) model, is a randomly evolving interface which, surprisingly enough, does not belong to either the Edwards-Wilkinson (EW) or the Kardar-Parisi-Zhang (KPZ) universality class. We show that 0-BD has a scaling limit, a new stochastic process that we call Brownian Castle (BC) which, although it is "free ", is distinct from EW and, like any other renormalisation fixed point, is scale-invariant, in this case under the 1:1:2 scaling (as opposed to 1:2:3 for KPZ and 1:2:4 for EW). In the present article, we not only derive its finite-dimensional distributions, but also provide a "global " construction of the Brownian Castle which has the advantage of highlighting the fact that it admits backward characteristics given by the (backward) Brownian Web (see [37, 16]). Among others, this characterisation enables us to establish fine pathwise properties of BC and to relate these to special points of the Web. We prove that the Brownian Castle is a (strong) Markov and Feller process on a suitable space of cadlag functions and determine its long-time behaviour. Finally, we give a glimpse to its universality by proving the convergence of 0-BD to BC in a rather strong sense. (c) 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.