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Preheat the oven to 375°.
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Heat and wide, shallow pan over medium heat, and add the butter. Sauté the onion and diced chard stems until lightly caramelized, 6 to 7 minutes.
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Add the garlic and chili flakes, and cook an additional 30 seconds or until aromatic.
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Stir in the yellow squash, and sauté until softened.
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Add the tomatoes and chard leaves, and cook until the greens are wilted.
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Mix in the dill and 1/2 cup of the parmesan cheese, and season with salt and pepper to taste.
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Use a spoon to create eight shallow wells in the vegetable mixture to hold the eggs. Crack an egg into each of the wells, and sprinkle them with salt and pepper. Bake in the oven until the egg whites are set and the yolks are still a bit loose, about 15 minutes, or up to 20 minutes for well-done yolks.
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Remove the pan from the oven, and top with the remaining parmesan cheese.
