Place eggs in a saucepan of boiling water and cook for 9 minutes for a medium-hard yolk. Immediately transfer to an ice bath, cool completely, peel, and slice into halves.
Prepare the dressing by whisking together the olive oil, lemon juice, ground sumac, honey, sea salt, and black pepper in a small bowl until emulsified.
Arrange the sliced cucumber, radishes, and shaved red onion across a large serving platter to create a base.
Gently flake the smoked trout fillets into large, bite-sized pieces and distribute them over the vegetables.
Nestle the halved eggs among the trout and vegetables.
Scatter the capers and fresh dill sprigs over the platter.
Drizzle the sumac dressing evenly over all components.
Serve immediately with toasted rye bread or crackers on the side.