Stack several snow peas and slice on the diagonal into 1/4-inch-wide strips. Repeat to slice remaining peas.
In a large bowl, whisk vegetable oil, soy sauce, sesame oil, ginger, sugar, and mustard until well combined. Add sliced snow peas and 1 tablespoon green onions; mix to coat. Cover and chill until cold, at least 1 hour, or up to 1 day.
Just before serving, mound salad on a platter and sprinkle with remaining tablespoon green onions and the sesame seeds.