Finely mince the garlic and grate the ginger on a Microplane until you have 1 teaspoon of fine pulp. Measure the soy sauce, water, brown sugar, honey, and rice vinegar into separate small cups, packing the brown sugar firmly.
Place the cornstarch in a small bowl and pour in the cold water. Stir with a fork or small whisk until smooth and milky with no dry clumps, then leave it by the stove.
Add the soy sauce, water, brown sugar, honey, rice vinegar, garlic, and ginger to the saucepan and whisk off the heat for 30 seconds. Bring to a gentle simmer over medium heat, then reduce to medium-low and simmer for 3 minutes, whisking occasionally.
Whisk the slurry again, then pour it into the saucepan in a slow, steady stream over medium heat while whisking constantly. Keep whisking for 1 to 2 minutes until the sauce turns glossy and coats the back of a spoon.
Remove from the heat and stir in the toasted sesame oil and sesame seeds. Taste, adding a splash of water if too salty or a few drops of rice vinegar if too sweet.
Let the sauce cool in the pan for about 10 minutes, then pour into a clean glass jar. Seal and refrigerate, or use right away on chicken, salmon, vegetables, or noodles.