A method and apparatus for upgrading a hydrocarbon feedstock is provided. The method includes the steps of (a) supplying a hydrocarbon feedstock to an oxidation reactor, wherein the hydrocarbon feedstock is oxidized in the presence of a catalyst under conditions sufficient to selectively oxidize sulfur compounds present in the hydrocarbon feedstock; (c) separating the hydrocarbons and the oxidized sulfur compounds by solvent extraction; (d) collecting a residue stream that includes the oxidized sulfur compounds; and (e) supplying the residue stream to a deasphalting unit.