Preheat oven to 350°F and generously butter 4 (6-ounce) ramekins or custard cups.
In a large skillet, heat oil over medium heat. Add garlic and cook 1 minute. Add Swiss chard; cover the skillet and cook, stirring frequently, until chard is tender, 8 to 10 minutes; add a few tablespoons water if the skillet begins to dry out. Remove from the heat and pour off any excess liquid.
Stir in 1/2 cup of the Parmigiano Reggiano and half the tomato. Spoon the mixture evenly into the ramekins. Break an egg into each ramekin and sprinkle with remaining Parmigiano Reggiano. Pile remaining tomato around eggs and season generously with salt and pepper. Place on a baking sheet and bake until egg whites are almost completely set, 15 to 20 minutes. Cool 5 minutes before serving.
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