Heat oil in a saucepan over medium heat. Cook and stir garlic in hot oil until fragrant, 2 to 3 minutes.
Stir tomato paste, sake, water, sugar, vinegar, miso paste, soy sauce, Worcestershire sauce, mustard, chili powder, ginger, and red pepper flakes with the garlic in the saucepan; bring to a simmer and cook, stirring frequently, until thickened, about 30 minutes.