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Preheat the oven to 450°F with a 9" or 10" cast-iron skillet inside.
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To prepare the pancake: In a medium bowl, whisk together the eggs, crème fraîche, and water until smooth.
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Add the flour, salt, and pepper, whisking until smooth; a few small lumps of flour can remain.
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Remove the skillet from the hot oven, add the butter, and return to the oven until melted (watch closely so the butter doesn’t burn). Remove the hot skillet from oven, swirl the butter in the pan to fully coat the sides, then pour in the batter.
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To bake the pancake: Immediately place the skillet in the oven and bake the pancake until dramatically puffed, 18 to 25 minutes. While the pancake is baking, prepare the topping.
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To prepare the topping: In a large nonstick skillet over medium heat, melt 1/2 tablespoon (7g) of the butter until it just starts to brown, then add the kale and toss a couple of times to coat.
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Cover the pan and cook for 1 minute, until the kale is wilted. Uncover, season with salt and pepper, and cook for another 3 minutes or so, tossing occasionally, until tender. Taste and adjust the seasoning as needed, then transfer the kale to a bowl and lower the heat to medium-low.
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Melt the remaining 1/2 tablespoon (7g) butter in the skillet. Crack in the eggs, sprinkle with salt and pepper, and cover the skillet. Cook for 2 to 3 minutes, until the whites are set but the yolks are still runny. Turn off the heat, uncover the skillet, and set aside until the pancake is ready.
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To finish the pancake: As soon as the pancake is done, slide it out of the skillet and top it with the kale, eggs, and spoonfuls of crème fraîche. Serve immediately.
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Storage information: Store any leftovers, well wrapped, in the refrigerator for a couple of days.