Cook eggs in a large saucepan of simmering water over medium heat until hard-boiled (10 minutes). Refresh under cold running water, peel, then halve lengthways and carefully remove yolks with a teaspoon. Place eggwhites on a tray lined with paper towels and refrigerate until required.
Press yolks through a fine sieve with a spatula into a bowl. Add mayonnaise, shallot, mustard, cayenne and Tabasco, season to taste, mix well, then carefully spoon or pipe into eggwhites.
Top a third of the eggs with smoked trout, radish and chives, another third with anchovies, smoked paprika and parsley, and the remaining eggs with prosciutto and cress, drizzle with olive oil, season to taste and serve.