Cut broccoli tops into florets and stems into two-inch-long, 1/4-inch-wide strips.
Heat the oil very hot in a large, heavy skillet. Add broccoli and crushed red pepper, and stir-fry until the broccoli just begins to soften--a little over a minute.
Combine orange juice, 1/4 cup water, sugar, ginger, and salt in a cup and add to the skillet. Bring to a boil and cook, stirring now and then, until the broccoli stems are almost tender. Add carrots and cook until tender.
Lower heat to low medium. Remove the broccoli and carrots. Dissolve cornstarch into 1/4 cup water, and stir into skillet. Cook and stir until sauce thickens. Return the vegetables to the pan along with the macadamia nuts. Heat through and serve.
