We consider direction-of-arrival estimation in hybrid analog/digital mmWave MIMO receivers that employ DFT beamspace processing with a limited number of RF chains. Building on beamspace ESPRIT, we develop a covariance-guided beam selection framework that reconstructs a virtual fully digital subarray, fits a structured signal-plus-noise covariance model, and uses the resulting denoised covariance to select, for each coarse sector, a small contiguous block of DFT beams under a beam-budget constraint. The selected beams feed a sparse beamspace Unitary ESPRIT stage, so that the overall complexity is dominated by a single low-dimensional ESPRIT call while retaining a large effective aperture. Monte Carlo simulations for a 32-element uniform linear array with three paths show that, relative to a standard sectorization-based beam selector built on the same DFT codebook and ESPRIT estimator, the proposed method attains near Cram\'er--Rao bound accuracy at moderate array signal-to-noise ratios, substantially reduces the gap to the bound and the failure rate, and offers favorable accuracy--runtime trade-offs under dynamic RF budgets and sector-edge stress tests.