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Make the honey-Dijon dressing: Whisk together vinegar, mustard, honey, and orange zest in a medium bowl. Slowly whisk in olive oil until well combined. Whisk in orange juice, 1 tablespoon at a time and tasting after each addition, until dressing has a balanced sweet-tart flavor. Season with salt to taste. Cover and refrigerate until ready to use.
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Make the fish-and-chips: Pour vegetable oil into a large Dutch oven (at least 6 quarts) to a depth of 2 inches; heat over medium to 375°F. Meanwhile, soak onion slices in a bowl of ice water for 20 minutes to soften their flavor; drain and set aside.
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Working in batches, fry potato slices, adding a few at a time to the oil to prevent them from sticking together and adjusting heat as needed, until lightly browned and crispy, about 5 minutes. Transfer chips to a paper towel–lined baking sheet using a slotted spoon or spider. Season with salt to taste; set aside.
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Separate the leaves from the head of lettuce, and arrange them on a platter. Slice the lettuce core, and sprinkle over the middle of the platter. Toss arugula, cucumber, tomatoes, fennel, scallions, reserved onion, and 1/4 cup dill in a large bowl with about 1/2 cup dressing. Add potato chips, and toss again. Season with salt and pepper to taste.
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Pile the arugula mixture in the middle of the platter, and scatter flaked trout over top; garnish with black pepper and remaining 1/4 cup dill. Drizzle with remaining dressing.