Initiates the repair of damaged proteins by catalyzing methyl esterification of L-isoaspartyl and D-aspartyl residues produced by spontaneous isomerization and racemization of L-aspartyl and L-asparaginyl residues in aging peptides and proteins. [protein]-L-isoaspartate + S-adenosyl-L-methionine = [protein]-L-isoaspartate alpha-methyl ester + S-adenosyl-L-homocysteine Monomer. Belongs to the methyltransferase superfamily. L-isoaspartyl/D-aspartyl protein methyltransferase family.