Cut the broccoli into small florets; trim and thinly slice the stalks. Heat the olive oil in a large non-stick frying pan or wok. Add the garlic (if using), capsicum, turnip and slices of broccoli stalk. Sprinkle in the sugar and salt to taste. Cook for 2–3 minutes, turning frequently.
Add the broccoli florets and stir. Pour in the water to provide a thin covering on the bottom of the pan. Cover and cook over a medium–high heat for 3–4 minutes. The broccoli should be just tender and bright green.
Stir in the basil, replace the lid and leave on the heat for a few more seconds. Serve immediately.