Manipulating free-space electron wave functions with laser fields can bring about new electron-optical elements for transmission electron microscopy (TEM). In particular, a Zernike phase plate would enable high-contrast TEM imaging of soft matter, leading to new opportunities in structural biology and materials science. A Zernike phase plate can be implemented using a tight, intense continuous laser focus that shifts the phase of the electron wave by the ponderomotive potential. Here, we use a near-concentric cavity to focus 7.5 kW of continuous-wave circulating laser power at 1064 nm into a 7 µm mode waist, achieving a record continuous laser intensity of 40 GW/cm2. Such parameters are sufficient to impart a phase shift of 1 rad to a 10 keV electron beam, or 0.16 rad to a 300 keV beam. Our numerical simulations confirm that the standing-wave phase shift profile imprinted on the electron wave by the intra-cavity field can serve as a nearly ideal Zernike phase plate.