Peel and pinch the carrots, peel the onion and roughly cut lengthways, peel the cloves of garlic and press or roughly chop.
Heat 10 tablespoons of oil in the wok, fry the carrot and onion pieces on high speed until they start to brown, then turn down the heat and add the garlic and chillies.
Carefully continue to fry briefly while stirring, being careful not to darken the garlic. Turn off the stove and add soy sauce, sugar and lime juice. Mix everything in a blender or in a tall container with a hand blender to a paste.
Heat the remaining 3 tablespoons of oil in the wok and fry the paste while stirring until it begins to turn brown. Possibly season with a tablespoon of soy sauce.
The paste can be kept closed in the refrigerator for about a month. It is mainly used in tom yam soup, but can also be used to flavor other (Thai) dishes.