Mix all ingredients until well combined. Refrigerate until ready to serve.
Heat oven to 375 degrees. Remove skin from salmon, check for bones. Cut salmon into 2-inch chunks. Place about 2/3 of salmon into a food processor and process until the texture of ground beef, about 10 pulses. Add egg and pulse once or twice. Add remaining salmon and process again, leaving visible small chunks of salmon, about 7 pulses. Transfer to a large bowl and with a spatula, stir in shallot, horseradish, mustard, lemon juice, salt and pepper. The mixture will be loose and a bit sticky.
Divide into six portions and shape into thick patties. Arrange on a well-greased baking sheet. Bake until patties are firm and cooked through, about 10 minutes.
To serve Big Sky Café-style, place arugula on a bun, top with salmon burger, Smoked Tomato Mayonnaise, two tomato slices and the top bun. Serve with kale chips on the side.