High-reflectance gratings promise new generations of vertical-cavity lasers that allow flexible control of the lasing mode properties and better integration. To date, conventional and polariton vertical-cavity lasers have been created with high-contrast gratings surrounded by air. Suspended in air, these gratings are delicate to fabricate and use, and are difficult for precise property control, electrical injection or thermal management. Here, we demonstrate a high quality vertical-cavity laser with a nonsuspended monolithic grating. High reflectance is achieved to allow the strong coupling regime, verified by angle-resolved photoluminescence measurements. We demonstrate polarized polariton lasing, manifested by a super-linear increase in the polariton emission and linewidth narrowing. We also demonstrate multi-wavelength operation of the polariton laser, with the wavelength controlled by design.