Ron Guth:
Proof coins of the 1820s are very rare, and the 1823/2 Cent is no exception. Early copper expert Denis Loring enumerated five different examples, of which four are listed in the PCGS CoinFacts Census above. All of the known examples show prooflike surfaces and an above-average strike, though all show weakness on the 7th through the 11th stars. Their appearance is much different than circulation strikes, even though they were all made from the same die pair (N-1).
The finest example appears to be the PCGS PR64BN from the Eugene Gardner Collection.