Heat 2 tbsp oil in a large wok or skillet over high heat. Add the garlic, ginger, and green chillies. Stir-fry for 30 seconds until fragrant, watching closely so the garlic does not burn.
Add the onion and stir-fry for 1 minute, until slightly softened but still with some bite.
Add the capsicum, cabbage, and carrot. Stir-fry on high heat for 2 to 3 minutes, keeping the vegetables crisp-tender.
Add the ketchup, soy sauce, chilli sauce, vinegar, pepper, sugar, and a pinch of salt. Stir together and cook for 1 minute.
Whisk the cornflour into the 1/4 cup water to make a slurry, then pour it into the pan along with the reserved pasta water or broth. Stir constantly and cook for 1 to 2 minutes, until the sauce turns glossy and coats the back of a spoon.