A method of recovering components from a hydrocarbon feedstock, the method characterized by the steps of: supplying the hydrocarbon feedstock to an oxidation reactor, the hydrocarbon feedstock comprising sulfur compounds and nitrogen compounds; contacting the hydrocarbon feedstock with an oxidizing agent in the oxidation reactor under conditions sufficient to selectively oxidize sulfur compounds and nitrogen compounds present in the hydrocarbon feedstock to produce an oxidized hydrocarbon stream that comprises hydrocarbons, oxidized sulfur compounds, and oxidized nitrogen compounds; separating the hydrocarbons, the oxidized sulfur compounds, and the oxidized nitrogen compounds in the oxidized hydrocarbon stream by solvent extraction with a polar solvent to produce an extracted hydrocarbon stream and a mixed stream, the mixed stream comprising the polar solvent, the oxidized sulfur compounds, and the oxidized nitrogen compounds, wherein the extracted hydrocarbon stream has a lower concentration of sulfur compounds and nitrogen compounds than the hydrocarbon feedstock; separating the mixed stream using a distillation column into a first recovered polar solvent stream and a first residue stream, the first residue stream comprising the oxidized sulfur compounds and the oxidized nitrogen compounds; supplying the first residue stream to a fluid catalytic cracking unit, the supplying further comprising feeding the first residue stream through a hydrotreater prior to supplying the first residue stream to the fluid catalytic cracking unit, the fluid catalytic cracking unit being operative to catalytically crack the oxidized sulfur and the oxidized nitrogen to produce regenerated catalyst and gaseous and liquid products and allow for recovery of hydrocarbons from the first residue stream; and recycling at least a portion of the liquid products to the oxidation reactor to selectively oxidize sulfur compounds in the liquid products, the portion of the liquid products comprising at least one of light cycle oils and heavy cycle oils. supplying the hydrocarbon feedstock to an oxidation reactor, the hydrocarbon feedstock comprising sulfur compounds and nitrogen compounds; contacting the hydrocarbon feedstock with an oxidizing agent in the oxidation reactor under conditions sufficient to selectively oxidize sulfur compounds and nitrogen compounds present in the hydrocarbon feedstock to produce an oxidized hydrocarbon stream that comprises hydrocarbons, oxidized sulfur compounds, and oxidized nitrogen compounds; separating the hydrocarbons, the oxidized sulfur compounds, and the oxidized nitrogen compounds in the oxidized hydrocarbon stream by solvent extraction with a polar solvent to produce an extracted hydrocarbon stream and a mixed stream, the mixed stream comprising the polar solvent, the oxidized sulfur compounds, and the oxidized nitrogen compounds, wherein the extracted hydrocarbon stream has a lower concentration of sulfur compounds and nitrogen compounds than the hydrocarbon feedstock; separating the mixed stream using a distillation column into a first recovered polar solvent stream and a first residue stream, the first residue stream comprising the oxidized sulfur compounds and the oxidized nitrogen compounds; supplying the first residue stream to a fluid catalytic cracking unit, the supplying further comprising feeding the first residue stream through a hydrotreater prior to supplying the first residue stream to the fluid catalytic cracking unit, the fluid catalytic cracking unit being operative to catalytically crack the oxidized sulfur and the oxidized nitrogen to produce regenerated catalyst and gaseous and liquid products and allow for recovery of hydrocarbons from the first residue stream; and recycling at least a portion of the liquid products to the oxidation reactor to selectively oxidize sulfur compounds in the liquid products, the portion of the liquid products comprising at least one of light cycle oils and heavy cycle oils.