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1
Bring a large pot of salted water to a simmer.
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2
Prepare the leeks: Trim leeks of outer layer and roots.
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3
Cut crosswise to divide leeks into white bottoms and green tops (remove and discard the tough gray-green parts).
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4
Soak leeks in a large bowl of lukewarm water, swishing to dislodge sand.
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5
Lift from water and drain.
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6
Add the white pieces to the pot and simmer for 8 to 10 minutes.
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7
Using tongs, remove the white pieces, then cook the green pieces for 4 to 5 minutes.
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8
Both white and green pieces should be tender when probed with a paring knife.
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9
Blot dry.
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10
Transfer to a baking dish in one layer.
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11
Let cool.
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12
Make the vinaigrette: In a small bowl, whisk together vinegar, mustard and garlic.
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13
Season with salt and pepper, then whisk in 6 tablespoons olive oil.
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14
Set aside.
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15
Heat oven to 375 degrees.
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16
In a mixing bowl, combine breadcrumbs, thyme and Parmesan.
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17
Add 2 tablespoons olive oil and salt and pepper; toss well.
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18
Spread crumbs on a baking sheet.
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19
Bake for 8 to 10 minutes, until crisp and golden.
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20
When cool, mix in 2 tablespoons parsley.
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21
Heat broiler.
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22
Brush leeks lightly with olive oil and place several inches from flame.
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23
Broil for about 5 minutes, until browned and lightly charred.
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24
Spoon vinaigrette evenly over leeks.
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25
Top with crumbs and egg.
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26
Sprinkle with remaining parsley.
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27
Serve warm.
