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1
Prepare a large bowl of ice water.
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2
In a large pot of boiling salted water, cook the leeks, covered, until tender, about 5 minutes.
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3
Using a slotted spoon, transfer the leeks to the ice water to cool.
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4
Drain well, then transfer the leeks to paper towels to dry, cut side down.
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5
In a small bowl, whisk the vinegar with the shallot, mustard and tarragon.
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6
Slowly whisk in 1/4 cup plus 2 tablespoons of the olive oil.
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7
Season the vinaigrette with salt and pepper.
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8
In a large skillet, heat the remaining 1/4 cup of olive oil.
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9
Working in batches, fry the speck over moderately high heat, turning once, until crisp around the edges, about 3 minutes.
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10
Drain on paper towels.
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11
Add the butter to the skillet and reduce the heat to moderate.
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12
Crack 2 eggs into the skillet and fry, basting the eggs with fat, until the whites are set and the yolks are still slightly runny, about 3 minutes.
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13
Transfer the fried eggs to a plate.
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14
Repeat with the remaining eggs.
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15
Season the fried eggs with salt and pepper.
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16
In a large bowl, coat the leeks with the vinaigrette, keeping them intact.
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17
Arrange the leeks on a platter or on individual plates and top with the speck and fried eggs.
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18
Drizzle any remaining vinaigrette on top, sprinkle with the chives and serve.
