A low-cost compact planar leaky-wave antenna (LWA) is proposed offering directive broadside radiation over a significantly wide bandwidth. The design is based on an annular metallic strip grating (MSG) configuration, placed on top of a dual-layer grounded dielectric substrate. This defines a new two-layer parallel-plate open waveguide, whose operational principles are accurately investigated. To assist in our antenna design, a method-of-moments dispersion analysis has been developed to characterize the relevant TM and TE modes of the perturbed guiding structure. By proper selection of the MSG for a fabricated prototype and its supporting dielectric layers as well as the practical TM antenna feed embedded in the bottom ground plane, far-field pencil-beam patterns are observed at broadside and over a wide frequency range, i.e., from 21.9 GHz to 23.9 GHz, defining a radiating percentage bandwidth of more than 8.5%. This can be explained by a dominantly excited TM mode, with low dispersion, employed to generate a two-sided far-field beam pattern which combines to produce a single beam at broadside over frequency. Some applications of this planar antenna include radar and satellite communications at microwave and millimeter-wave frequencies as well as future 5G communication devices and wireless power transmission systems.