How to Make It
In a medium saucepan, heat 2 tablespoons of the oil. Add the onion, garlic and kimchi and cook over moderate heat, stirring occasionally, until softened and golden, about 8 minutes. Scrape the mixture into a food processor and add the tomatoes; puree until smooth.
In the saucepan, heat the remaining 2 tablespoons oil. Add the tomato paste and sugar and cook, stirring, until lightly caramelized, about 3 minutes. Add the tomato mixture and basil, cover and cook over moderately low heat, stirring occasionally, until thickened, about 30 minutes. Season with salt.