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Preheat the oven to 400°F / 200°C.
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Use 2 slices of prosciutto to line each of 8 standard muffin cups (it’s best to use 2 muffin pans each with 12 cups so that each set of prosciutto slices do not overlap the others).
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Set the muffin pans on large rimmed baking sheets to catch any drips and bake for 18 minutes, or until the prosciutto shrinks, becomes crisp, and forms cups.
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Meanwhile, bring a large skillet of water to a simmer over medium heat. Stir in the vinegar.
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Crack one egg into a coffee cup or small bowl and then gently transfer the egg to the simmering water. Repeat with 3 more eggs.
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Cook the eggs for about 3 minutes, or until the whites are set but the yolks are still runny.
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Using a slotted spoon, carefully remove the eggs from the simmering water and set them on a paper towel to drain the excess water.
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Repeat with the remaining 4 eggs.
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Meanwhile, melt the butter in a large sauté pan over high heat. Add the spinach and sauté for 2 minutes, or just until the spinach wilts.
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Set the toasted bagel halves cut side up on 4 plates. Spoon the wilted spinach atop the bagels, dividing evenly. Set the prosciutto cups atop the bagels. Spoon the eggs into the prosciutto cups and serve.