Preheat the oven to 350 degrees F. Butter the ramekins.
Heat the oil in a large skillet over medium heat until hot. Add the onion and cook, stirring, until golden, 6 to 8 minutes. Stir in the kale, 1 teaspoon salt and a couple turns of pepper and cook until tender, about 6 minutes. Divide the kale mixture evenly among the prepared ramekins. Sprinkle with the Cheddar.
Separate the egg whites and yolks. Whisk together the yolks, milk and 1/2 teaspoon salt in a large bowl. In a separate bowl, beat the egg whites and 1/4 teaspoon salt with an electric mixer until they hold soft peaks, being careful to not overbeat. Then gently fold the whites into the yolk mixture. Divide the egg batter evenly among the ramekins and bake until the eggs are set and puffed, about 25 to 30 minutes. Serve immediately.
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