In a large skillet over medium heat, add the oil. Add the onions, zucchini and red pepper flakes. Cook until the vegetables just begin to soften, 3 to 4 minutes. Add the ham and let cook another 3 to 4 minutes. Season with salt and pepper.
Crack the eggs into a bowl and beat them, adding a pinch of salt and pepper. Push the vegetables to the side of the skillet, add the eggs and cook until just set. Mix the eggs and vegetables together.
Add the rice to the skillet with the vegetables and egg and cook, stirring frequently, until the rice is hot. Reserve 1 cup of the cooked rice for the Round 2 Recipe Stuffed Cabbage Rolls, or another use. Transfer to a serving dish and serve immediately.