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Working ahead, make the cream cheese spread. First, roast the red pepper. This can either be done over an open gas flame or under the broiler. To roast over flame, set pepper over a medium-high flame; use tongs to turn pepper until it is blackened all over. For the broiler, turn broiler to high, set pepper on a foil-lined broiling pan and broil. Checking every few minutes, use tongs to turn pepper until it is blackened all over. Set roasted pepper in a paper bag, seal, and steam for 10 minutes. Peel blackened skin off under cold running water, remove stem, and seeds. Pat dry.
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Pulse to combine roasted pepper, cream cheese, garlic, sea salt, pepper, and paprika in the bowl of a food processor. Scrape down sides, turn processor on, and process just until smooth. Spoon into a bowl, stir in dill, cover, and chill in the fridge for a few hours or preferably overnight.
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To assemble sandwiches, spread 1 - 2 tablespoons red pepper cream cheese on each slice of bread. Layer one of the slices with a handful of arugula, half the salmon, and several layers sliced radishes. Sprinkle a pinch of sea salt over radish layer. Top with other bread slice, wrap tightly in parchment, and slice in half with a very sharp chef's knife. Repeat for second sandwich.