Process shrimp, egg, and salt in a food processor until mostly smooth.
Add scallions and pulse until incorporated into the shrimp mixture.
Spread the shrimp mixture evenly on bread triangles.
Dip each piece in breadcrumbs, coating both sides thoroughly.
Heat oil to medium-high heat in a large skillet or deep fryer.
Fry the shrimp toast until golden brown on both sides, about 2-3 minutes per side.
Remove and drain on paper towels.
Serve immediately while warm.