1. Preheat oven to 400°F. Warm oil in a large nonstick, ovenproof skillet over medium-high heat. Sauté garlic until fragrant, about 30 seconds. Stir in chard. Cover and cook, stirring twice, until chard is tender, about 5 minutes. Remove cover; stir in ham.
2. Place eggs in a large bowl; season with salt and pepper and whisk to blend. Pour eggs over chard and ham in skillet. Stir to distribute ingredients as evenly as possible before eggs begin to set.
3. Cook on top of stove, lifting sides of frittata with a spatula to let uncooked eggs flow underneath, until lightly browned around edges, 3 to 5 minutes. Sprinkle frittata with Parmesan, transfer skillet to oven and bake, uncovered, until firm in center and slightly browned on top, about 10 minutes. Cut into wedges and serve.