The one-to-all broadcast is the most primary collective communication pattern in a multi-computer network. This paper studies this problem in a circuit-switched torus with α-port capability, where a node can simultaneously send and receive α messages at one time. This is a generalization of the one-port and all-port models. We show how to efficiently perform broadcast in tori of any dimension, any size, square or nonsquare, using near optimal numbers of steps. The main techniques used are: (1) a "span-by-dimension" approach, which makes our solution scalable to torus dimensions, and (ii) a "squeeze-then-expand" approach, which makes possible solving the difficult cases where tori are non-square. Existing results, as compared to ours, can only solve very restricted sizes or dimensions of tori, or use more numbers of steps.