Set a rack in the upper third of oven and preheat broiler.
In a small bowl, whisk eggs, cream, salt, and pepper until combined.
In a 10-inch ovenproof saute pan, melt 2 tablespoons butter over medium-high heat. Add onions and peppers and cook, 7 to 8 minutes, stirring as needed, until soft. Add zucchini and spinach (or other chopped fresh vegetables) and cook, 2 minutes. Add ham and cook until warmed through, 1 minute. Add remaining tablespoon butter and, when melted, add egg mixture. Sprinkle fresh herbs over eggs and top with Swiss cheese. Reduce heat to medium and cook eggs, undisturbed, 3 minutes, or until surface of eggs begins to bubble and bottom starts to set. Immediately place pan in oven and broil eggs until golden brown on top and sides, 3 to 4 minutes. Remove pan from oven. Using a rubber spatula, loosen frittata from sides of pan. Tilt pan and gently slide frittata onto a serving plate. Garnish with Parmigiano and serve hot or warm.