Drain the canned salmon and remove any remaining bones; flake the salmon into a medium mixing bowl.
Add the beaten egg, diced sweet onion, chopped parsley, breadcrumbs, Dijon mustard, salt, and black pepper to the bowl; mix until evenly combined.
Shape the mixture into 8 small, evenly sized patties.
Heat the olive oil in a skillet over medium heat until shimmering.
Cook the patties in the skillet, about 3–4 minutes per side, until golden brown and cooked through.
Assemble each slider by placing a patty on a whole-wheat slider bun and topping with romaine lettuce, sliced tomato, and red onion.
Serve immediately with condiments of choice.