We present the energy scaling of a sub-two-cycle (10.4 fs) carrier-envelope-phase-stable light source centered at 1.76 µm to 1.9 mJ pulse energy. The light source is based on an optimized spectral-broadening scheme in a hollow-core fiber and a consecutive pulse compression with bulk material. This is, to our knowledge, the highest pulse energy reported to date from this type of sources. We demonstrate the application of this improved source to the generation of bright water-window soft-X-ray high harmonics. Combined with the short pulse duration, this source paves the way to the attosecond time-resolved water-window spectroscopy of complex molecules in aqueous solutions.