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1
Preheat the oven to 425F.
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2
Scrub the new potatoes to remove any excess dirt. Slice them crosswise, into kind of thick potato chips. Meanwhile, give the asparagus a nice soak, to remove any grit that might be clinging to them.
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3
Toss both the new potatoes and the asparagus with 2 tablespoons of the olive oil, sea salt and pepper. Move everything to a parchment paper-lined baking sheet, making sure not to crowd, and then transfer the baking sheet to the oven.
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4
Cooking time is going to depend on the thickness of your potato chips, and the thinness of your asparagus spears. (My potatoes took about 30 minutes, while the asparagus took 15.) I would check the vegetables at 10 minute intervals. Remove items from the oven when they look finished to you, and set them aside.
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5
While the vegetables are cooking, slice up the red onion, as thinly as possible. Move the slices to a small bowl, and add 1 tablespoon of vinegar. Fill the remainder of the bowl with cold water, so that the onion slices are completely covered. Cover the bowl with plastic wrap, and set aside. (I kept mine this way for about 30 minutes, just to lessen the sharpness of the onion.)
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6
Wash and dry your lettuce.
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7
Mix your vinaigrette: In a small bowl, spoon in the mustard. Add a pinch of sea salt and pepper, and then add the remaining tablespoon of white vinegar. Stir everything together with the back of a spoon, until the salt is dissolved. Add the remaining 3 tablespoons of olive oil slowly, whisking as you go, until the whole thing is emulsified. Set the bowl aside.
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8
Cut your bacon into little lardons. (Basically, cut it crosswise into 1/4-1/3 inch pieces.)
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9
Heat a wide, non-stick pan on medium. When it is nice and hot, fry up your lardons. When they look crispy, but not burnt, remove them to a paper towel-lined plate. When you've removed all the lardons, lower the heat to a simmer, but don't turn it off completely.
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10
Drain and dry the onion slices.
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11
In a large bowl, toss the lettuce, potatoes, asparagus, onion and lardons together with the mustard vinaigrette. (If the vinaigrette has separated a little, just give it a little whisk.) Separate the salad onto four plates.
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12
Turn the heat on the lardon pan back to medium. When the lardon fat is very gently bubbling, add the eggs, one at a time. (I like to top mine with a little more sea salt and pepper as they cook.) Cook them for about 1 minute on each side, so that the whites are cooked, but the yolk is still runny. Top each salad plate with an egg. Voila!
