Preheat the broiler and place the top rack 4 to 5 inches from the broiler element.
In a large bowl, whisk together the eggs, cream, 1/4 teaspoon of the salt, and 1/8 teaspoon of the pepper until the eggs are frothy. Set aside.
In a 10-inch nonstick ovenproof skillet, melt the butter over medium-high heat. Add the onions and green and red bell peppers and cook, stirring, until the vegetables are soft, 3 to 4 minutes. Add the ham and stir well. Add the green onions, garlic, parsley, remaining 1/4 teaspoon of the salt, and 1/8 teaspoon pepper and cook, stirring, until the garlic is fragrant, about 30 seconds.
With the pan over medium heat, pour the egg mixture over the vegetables and ham, and evenly place the cubed cheeses across the surface. Cook, lifting with a rubber spatula to let the eggs flow underneath, until the edges are set but the middle still is loose, 3 to 4 minutes.
Remove from the heat and sprinkle the Parmesan over the top. Place under the broiler until the eggs are slightly puffed and the cheese is golden brown, 2 to 3 minutes, watching carefully to prevent from overcooking.
Remove from the oven and carefully slide the frittata out onto a large serving platter. Garnish with additional parsley and chopped green onions, slice, and serve immediately.
Yield: 6 servings