A low-cost planar leaky-wave antenna (LWA) offering directive antenna beam patterns as well as linear beam scanning through broadside is proposed in this letter. The design is based on a one-sided annular slot grating placed on a duallayer grounded dielectric slab with an integrated TM0 antenna feed system in the bottom ground plane. By appropriate selection of the width and the period of the top radiating annular slots, as well as the substrates, the structure is optimized to excite and perturb the dominant TM mode for the generation of directive beam patterns that can scan with frequency in the far-field. In particular, the antenna parameters are chosen to obtain a narrow open stop-band frequency range at broadside as well as control the dispersive scanning behavior. A method-of-moments dispersion analysis has also been developed to assist in the design and fully characterize the proposed antenna. These results are complemented by full-wave simulations and measurements of a LWA prototype offering realized gain values in excess of 14 dBi with scanning through broadside at 23.5 GHz.