Although most markets stock hoisin sauce, you might enjoy making your own. This sauce will keep, refrigerated, for 1 month.
Rinse the azuki beans in cold water and drain. Pick through the beans and discard any discolored or broken beans.
Bring 5 cups of water to a boil in a medium pan. Add the beans and reduce the heat to low. Simmer, uncovered, until the beans are very tender, 1-1/2 to 2 hours.
Drain the beans if there is any water remaining. When cool, transfer to a food processor and purée until smooth. At this point, the bean paste may be frozen for 2 months or stored, covered, in the refrigerator for up to 1 week.
Heat the oil in a large pan over medium heat. Add the garlic and sauté, stirring frequently, until the garlic turns golden and fragrant, about 2 minutes. Stir in 1 cup of the bean paste, sugar, water, vinegars, and soy sauce. Cook over low heat until the mixture thickens, 10 to 15 minutes. Add the chile sauce and cool.
Transfer the cooled sauce to a glass jar or plastic container, cover tightly, and refrigerate for 1 month or freeze for 3 months.