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1
Preheat the oven to 375u00b0F.
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2
Place the cubed brioche on a rimmed baking sheet and toast until golden brown, shaking the pan halfway through to toast evenly, 8 to 10 minutes.
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3
Bring a pot of salted water to a boil. Add the asparagus and cook until just tender, about 5 minutes.
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4
Drain and plunge asparagus in a large bowl of ice water to stop the cooking. Drain well, then slice spears in thirds.
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5
For the dressing, whisk together the vinegar, mustard, shallot, lemon zest, salt, pepper, dill and one teaspoon of the chopped chives in a medium bowl. Gradually whisk in the olive oil until the vinaigrette is emulsified. Set aside.
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6
Place the frisee and field greens in a large bowl. Add the croutons.
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7
Break up the smoked trout, discarding the skin, and add to the lettuce with the sliced asparagus. Set aside.
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8
Prepare the pan for poaching the eggs: fill a large shallow pan halfway with water and bring to a boil; break an egg into a small saucer, taking care not to break the yolk, and slide egg into the water; repeat with remaining eggs and lower the heat to a simmer.
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9
Poach until the whites are set and the yolks begin to thicken but are not hard, about 4 minutes.
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10
Remove the eggs with a slotted spoon and drain them on paper towels. Depending on the size of your pan, you may need to poach the eggs in two or three batches.
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11
Note: If you are making these ahead, remove eggs to a bowl of iced water and hold there until ready to serve; refresh eggs briefly in simmering water.
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12
Toss the salad with the vinaigrette to coat lettuce, croutons, trout and asparagus evenly.
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13
Divide among 6 plates.
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14
Place a poached egg on top of each salad and garnish with the remaining chopped chives.
