Heat oven to 400° F. Spread the walnuts on a rimmed baking sheet and toast until fragrant, 6 to 8 minutes. Let cool, then roughly chop.
In a large bowl, combine the corn, Feta, jalapeños, oil, lime juice, walnuts, ½ teaspoon salt, and ¼ teaspoon pepper.
In a food processor, pulse the salmon 3 or 4 times, until coarsely chopped but still somewhat chunky.
Add the scallions, ½ teaspoon salt, and ¼ teaspoon pepper and pulse just to combine. Form the mixture into ¾-inch-thick patties.
Heat grill to medium-high. Oil the grate. Grill the patties, turning once, until opaque throughout, 2 to 4 minutes per side.
Serve on the rolls, topped with the avocado and cilantro (if desired).