Heat a wok or frying pan over medium heat. Pour in the sesame seed oil and swirl the pan to coat the bottom completely.
Add the cauliflower, broccoli, onion and thyme to the oil. Cook, stirring occasionally, for about three minutes.
Drizzle in a tablespoon of water. Cover the pan and allow the vegetable to soften in the steam for three to four minutes.
Uncover the pan. Stir in the garlic and nuts. Season with salt and pepper. Continue cooking for another minute or two until the mixture is dry.
Taste. Add more salt and pepper, if needed.
Off the heat, toss in the sesame seeds and parsley.
Serve the cauliflower and broccoli "fried rice" while hot.