To prepare the salmon carpaccio: Slice the salmon crosswise into 4 equal pieces. Paint each slice lightly with olive oil and place between 2 pieces of waxed paper. Using a meat mallet or wine bottle, with light tapping motions, very gently pound the salmon to about 1/16- inch thickness. Refrigerate in the waxed paper until ready to serve.
02Put the shallot, lemon zest and lemon juice in a small bowl. Season with salt and pepper. Add the capers. Whisk in 3 tablespoons olive oil.03To prepare the halibut tartare: Dice the halibut as small as possible, put it in a bowl and put the bowl on ice.04Just before serving, season the halibut with salt and pepper. Gently stir in the scallions, cucumber, jalapeño, olive oil and lime juice.05For each serving, carefully peel one sheet of waxed paper from the salmon and invert onto a chilled plate. Remove the remaining waxed paper. Sprinkle the salmon lightly with salt. Drizzle with the lemon-caper oil and sprinkle with the chives and nasturtium petals.06Spoon a 2-ounce mound of halibut tartare onto each plate, next to the salmon. Sprinkle with the dill.