Build and tend an active fire in a firepit, bringing it to medium-high heat with no live flame and a growing bed of glowing hot coals. Position grill grate directly over fire. Alternatively, light charcoal grill or fire up gas grill to highest setting.
Put salmon, dill, Sriracha Pickled Red Onions and salt in food processor. Pulse for a few seconds at a time until mixture is a bit chunky and just comes together. Do not purée.
Divide mixture into 4 equal portions and shape into thick patties. The burgers may seem like they’ll fall apart, but they’ll firm up as they cook through. Place each patty on separate square of parchment paper. Cook immediately or refrigerate until fire is ready.
Stoke fire and wait just until the flames die down, while the fire’s fiercest heat remains in its glowing active embers. Invert burgers onto grill with parchment still attached. Remove paper and discard. Sear burgers over fire until golden brown on bottom, 2 to 3 minutes. Flip them over and brown second side, another 2 to 3 minutes.
While burgers are cooking, toast buns cut-side down over fire.
Transfer Salmon Burgers to bottom of each bun. Top with a leaf or two of lettuce, a few tomato slices and a tangle of sriracha pickled red onions. Finish with bun tops.