For the vinaigrette, whisk together vinegar, mustard, shallot, lemon zest, salt, pepper, dill and 1 teaspoon chopped chives in a medium bowl. Gradually whisk in olive oil until the vinaigrette is emulsified. Set aside. For the salad, preheat oven to 375°F. Place cubed brioche on a rimmed baking sheet and toast until golden brown, shaking the pan halfway through to toast evenly, 8 to 10 minutes.

Bring a pot of salted water to a boil. Add asparagus and cook until just tender, about 5 minutes. Drain and plunge asparagus in a large bowl of ice water to stop the cooking. Drain well, then slice spears in thirds. Place frisée and field greens in a large bowl. Add croutons. Break up smoked trout, discarding skin, and add to lettuce with sliced asparagus. Set aside.

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. Poach until whites are set and yolks begin to thicken but are not hard, about 4 minutes. Remove 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.

Toss the salad with the vinaigrette to coat lettuce, croutons, trout and asparagus evenly. Divide among 6 plates. Place a poached egg on top of each salad and garnish with remaining chopped chives.