Heat vegetable oil in a small saucepan over medium heat. Add garlic and ginger and cook for about 30 seconds, stirring constantly, until fragrant but not browned. Pour in soy sauce, brown sugar, rice vinegar, hoisin sauce, chili paste, and water. Whisk until the sugar fully dissolves.
Increase the heat slightly to bring the sauce to a gentle simmer. Stir occasionally to prevent sticking.
Make the Cornstarch Slurry: In a small bowl, whisk cornstarch with 2 tablespoons of cold water until smooth, with no lumps.
Slowly pour the cornstarch slurry into the simmering sauce while whisking constantly. Keep whisking for 1 to 2 minutes, until the sauce is glossy and thick enough to coat the back of a spoon.
Remove the pan from heat and stir in sesame oil. Taste the sauce and adjust with more chili paste or sugar as needed. Pour the sauce over crispy chicken, tofu, or vegetables right away, or let it cool and store for later.