Bring a large saucepan 3/4 full of water to a boil. Add the cauliflower and broccoli and return to a boil. Cook until the vegetables are tender-crisp, about 1 minute. Drain the vegetables and then plunge them into a bowl of ice water to stop the cooking. Drain again and set aside. In a small bowl, stir together the oyster sauce, water and chili paste. Set aside.
In a large, heavy nonstick frying pan, heat the olive oil over medium-high heat. Add the ginger and garlic and saute for 30 seconds. Don't let the garlic brown. Add the carrot and saute for 1 minute. Add the cauliflower and broccoli and stir until just tender, about 2 minutes. Add the oyster sauce mixture and toss until the sauce is evenly distributed and the mixture is heated through, about 1 minute.
Transfer to a warmed serving dish and garnish with the green onion. Serve immediately.