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1
Separate the eggs, reserving each yolk in its shell and combining 2 whites in a cup. Refrigerate the remaining 2 whites for another use.
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2
In a cold medium skillet, combine the oil, garlic, peperoncini, and oregano. Turn on the heat and warm over medium-high heat until the garlic begins to fry (without browning) and the mixture becomes fragrant, about 2 minutes.
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3
Raise the heat to high, then use your hands to crush each tomato into the pan, allowing the juice to fall into the skillet. Season lightly with salt and pepper. Fry the tomatoes, continuing to break them up with the fork. Cook until they concentrate and no longer look watery, 2 to 3 minutes. Add the basil.
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4
Lower the heat to medium and stir in the egg whites. Cook until the whites become opaque and firm, thickening the tomato sauce, about 1 minute.
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5
Turn off the heat. Using the back of a spoon, make 4 indentations in the sauce, allowing a few inches around each. Slip an egg yolk into each indentation. Draw the sauce in from the edges of the pan around each of the yolks. Cover the skillet and leave it on the stove, heat off, until the yolks are just warmed through and beginning to set, about 3 minutes for runny yolks.
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6
Gently spoon some sauce and a yolk onto each piece of toast and serve immediately. I find rubbing some olive oil on the spoon helps prevent breaking the yolk.
