Gather the ingredients.

In a large cup or small bowl, combine coconut milk, soy sauce, lime juice, chilli flakes, and brown sugar, stirring well to dissolve the sugar. Taste test, keeping in mind that the first taste should be spicy-salty, followed by sweetness and the rich taste of the coconut milk. Adjust these flavors to suit your taste, adding more lime juice if too sweet or salty (note that it will be less salty when combined with the vegetables).

Warm a wok or large frying pan over medium-high heat.

Add 2 tablespoons oil and swirl around, then add the shallots, garlic, ginger, and chilli flakes.

Stir-fry 1 to 2 minutes, then add the carrot, mushrooms, optional cauliflower, and ¼ of the stir-fry sauce. Continue stir-frying 2 to 3 minutes.

Add the broccoli and red pepper plus enough stir-fry sauce to gently simmer vegetables (about 2 minutes). This is meant to be a "saucy" stir-fry that is never dry so the sauce can flavor the rice or noodles it is served with.

Finally, add the bok choy or Chinese cabbage. Add more of the stir-fry sauce as needed, almost enough to just cover vegetables in sauce. Simmer until bok choy or cabbage is cooked but still bright green with some crispness (2 to 3 minutes more).

Remove from heat and taste test. If not salty enough, add a little more fish or soy sauce. If too salty or sweet, add a squeeze of lime juice. Add more sugar or chile if desired. Top with fresh basil and serve over Thai jasmine rice or Thai coconut rice.