Glycosyltransferase that generates the core 1 O-glycan Gal-beta1-3GalNAc-alpha1-Ser/Thr (T antigen), which is a precursor for many extended O-glycans in glycoproteins. an N-acetyl-alpha-D-galactosaminyl derivative + UDP-alpha-D-galactose = a beta-D-galactosyl-(1->3)-N-acetyl-alpha-D-galactosaminyl derivative + H(+) + UDP Protein modification; protein glycosylation. Homodimer; disulfide-linked. Belongs to the glycosyltransferase 31 family. Beta3-Gal-T subfamily.