Cut the stems off the Thai chili peppers. Place the peppers (seeds and all!), garlic cloves, ginger, vinegar and water in a blender. Blend until the peppers, garlic and ginger are finely minced.
Pour the sauce in a pot and stir in the sugar. Bring it to a boil and keep it at a rolling boil for 10 minutes, stirring often.
Remove from the heat and stir in the grated carrot and daikon.
In a small bowl, mix the corn starch and 2 tbsp of water until the corn starch dissolves. Pour it into the sauce, stirring with a whisk. Keep stirring until the sauce thickens. If the sauce does not thicken enough, it may be necessary to put it back on the heat for a few minutes, stirring constantly, until it thickens.