How to Make It
Preheat grill to medium (about 400°F). Stir together mayonnaise, green onions, mustard, zest, juice, hot sauce, and 1/4 teaspoon of the salt in a medium bowl. Cover and chill until ready to use.
Toss together shrimp, 2 tablespoons of the olive oil, and remaining 1 teaspoon salt in a large bowl. Grill shrimp, covered with grill lid, just until shrimp turn pink, 2 to 3 minutes on each side. Brush hoagie buns with remaining 1 tablespoon olive oil, and grill, cut side down, until slightly charred and crisp, about 2 minutes.
Spread cut sides of rolls evenly with rémoulade sauce. Layer shrimp and lettuce on bottom halves of rolls; cover with roll tops. Serve with remaining rémoulade sauce.