We present two epochs of observations of TW Hya from the high-dispersion near-IR spectrograph ARIES at the MMT. We detect strong emission from the Brackett gamma transition of hydrogen, indicating an accretion rate substantially larger than previously estimated using hydrogen line emission. The Brackett gamma line-strength varies across our two observed epochs. We also measure circumstellar-to-stellar flux ratios (i.e., veilings) that appear close to zero in both epochs. These findings suggest that TW Hya experiences episodes of enhanced accretion while the inner disk remains largely devoid of dust. We discuss several physical mechanisms that may explain these observations.