We present the electronic characterization of single-layer 1H-NbSe2 and 1H-TaSe2 grown by molecular beam epitaxy (MBE) using a combined angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy/spectroscopy (STM/STS), and density functional theory (DFT) calculations. We demonstrate that 3×3 CDW order persists despite distinct changes in the low energy electronic structure highlighted by the reduction in the number of bands crossing the Fermi energy (EF) and the corresponding modification of Fermi surface (FS) topology. Enhanced spin-orbit coupling and lattice distortion in the single-layer limit play a crucial role in the formation of CDW order. Our findings provide a deeper understanding of the nature of CDW order in the 2D limit.