Wipe out now-empty skillet with paper towels and melt remaining 2 tablespoons butter over medium-low heat. Add garlic and cook, stirring occasionally, until lightly golden, about 2 minutes. Stir in chard and increase heat to medium-high. Cover and cook until chard is wilted but still bright green, about 2 minutes. Uncover and cook, stirring frequently, until liquid evaporates, about 1 minute. Transfer chard to gratin dish and spread evenly over tomatoes.
Whisk cornstarch and 1/2 teaspoon salt together in medium bowl. Whisk in half-and-half, eggs, and 3/4 cup Manchego until thoroughly combined. Pour egg mixture over tomatoes and greens. Sprinkle with remaining 1/4 cup Manchego. Bake gratin on middle rack until toothpick inserted in center comes out clean, 30 to 40 minutes, rotating dish halfway through baking. Remove gratin from oven.
Heat broiler. Broil gratin on top rack until cheese is golden brown, about 2 minutes. Let gratin cool until custard has set up, about 5 minutes. Serve.