Is there any two surface fully corrected lens design for order from a lens grind from a shop ?
I've had a copy of this paper for years. It is a good summarizing document on two-surface designs within his field of expertise, but doesn't provide much detail. His references are more interesting.
To fully correct (assuming you mean as an imaging objective), the answer is no. Think in mathematical terms: The number of variables available vs the number of aberrations.
The Cooke Triplet provides the minimum number of variables to fully correct all third-order aberrations as well as focusing an image. Even then, higher order aberrations limit the lens speed.
Two-surface mirror telescopes achieve correction over a limited field of view, but cannot fully correct all third order aberrations. Usually field curvature and distortion are left uncorrected. The speed of the scope (f/#) is limited by the need to control higher order aberrations.
The Double Gauss is the minimum design form to correct all third order anerrations and control higher order aberrations at all lens speeds.