Beat the eggs in a medium bowl or pot. Add the milk, cheese, salt, pepper, and rosemary and mix well. Set aside. Heat the oil in a skillet over high heat on a camp stove. Add the onion and cook, stirring, for about 2 minutes, until it is beginning to soften. Reduce the heat to medium-high, add the mushrooms and bell pepper, and cook for about 5 minutes more, until the onion is translucent and the mushrooms and pepper soften. Add the polenta and cook, stirring, for about 2 minutes more, until heated through. Spread the polenta mixture into an even layer, reduce the heat to medium-low, and pour the egg mixture over the top. Cover and cook for about 12-15 minutes, stirring once or twice during cooking, until cooked through. Serve immediately.