Cut the salmon into large chunks, and put about half into the bowl of a food processor with the mustard. Turn the machine on, and let it run until the mixture becomes pasty. Scrape down sides when needed.
Add the shallots and the remaining salmon, and pulse the machine until the fish is chopped and well combined with the puree. Be careful to not make the mixture too pureed.
Scrape the mixture into a bowl, and, by hand, stir in the bread crumbs, capers, and some salt and pepper. Shape into eight burgers or 16 sliders.
Place the butter or oil in a 12-inch nonstick skillet, and turn the heat to medium-high. When the butter foam subsides or the oil is hot, cook the burgers for 2 to 3 minutes a side, turning once. To check for doneness, use an instant read thermometer and register to 145° F in the center. Be careful not to overcook.
Serve on a bed of greens, on buns, or by themselves. Add lemon wedges and a side of sweet potato fries.