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1
Preheat oven to 450F.
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2
Add asparagus, 2 teaspoons oil and 1/4 teaspoon each salt and pepper in a large bowl, and toss until well mixed and coated.
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3
Transfer to a large rimmed baking sheet in a evenly single layer.
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4
Roast, stirring once or twice until very tender but still crispy, 16 to 18 minutes.
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5
Meanwhile, whisk the remaining olive oil, salt and pepper to taste, lemon zest, lemon juice, shallot and dry mustard in the bowl.
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6
Set aside 4 teaspoons of the dressing in a small bowl.
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7
When the asparagus is done, set aside to let cool while you poach the eggs.
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8
Break each egg into its own small bowl.
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9
Bring a Dutch oven with 2 inches of water to a boil.
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10
Pour in the vinegar.
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11
Reduce to a gentle simmer.
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12
Submerging the lip of each bowl into the simmering water, slowly pour in the eggs, one at a time.
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13
Boil for 4 minutes for soft set, 5 to 6 minutes for medium set and 8 minutes for hard set.
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14
With a slotted spoon, remove the eggs from water to a clean kitchen towel to let drain for 1 or 2 minutes.
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15
Add arugula in the large bowl, and toss with remaining dressing until well coated.
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16
Divide the salad among 4 plates.
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17
Arrange asparagus and a poached egg on top of each plate and drizzle with 1 teaspoon of the reserved dressing.
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18
Sprinkle some parmesan cheese on top.
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19
Serve with crusted bread if desired.
