Step 1In the bowl of a food processor, pulse the salmon cubes several times until coarsely ground (there will still be flakes of salmon). Remove the ground salmon to a large bowl, and stir in the capers, bread crumbs, lemon juice, pepper, salt and egg until the mixture is uniform and fully combined. Divide the mixture into 4 patties.
Step 2In a large saute pan, melt the butter over medium-high heat. Add the burgers (do not crowd, they can be cooked in batches) and saute, adjusting the heat as needed, until the burgers are golden on the outside and cooked throughout, 2 to 2 1/2 minutes per side.
Step 3Prepare the burgers: Brush the insides of each toasted bun with tartar sauce, and spoon a little coleslaw on the base of the bun. Place a burger on the slaw, then the bun top. Serve immediately.