Ethernet-style broadcast is a pervasive style of computer communication. In this style, the medium is a single nameless channel. Previous work on modelling such systems proposed a first order process calculus called CBS. In this paper, we propose a fundamentally different calculus called HOBS. Compared to CBS, HOBS 1) is higher order rather than first order, 2) supports dynamic subsystem encapsulation rather than static, and 3) does not require an "underlying language" to be Turing-complete. Moving to a higher order calculus is key to increasing the expressivity of the primitive calculus and alleviating the need for an underlying language. The move, however, raises the need for significantly more machinery to establish the basic properties of the new calculus. This paper develops the basic theory for HOBS and presents two example programs that illustrate programming in this language. The key technical underpinning is an adaptation of Howe's method to HOBS to prove that bisimulation is a congruence. From this result, HOBS is shown to embed the lazy λ-calculus.