In a small saucepan, boil 1 cup water. In a large bowl, combine the flour and salt. Stirring, slowly pour in 3/4 cup of the boiling water until just incorporated. Knead briefly until a dough forms, adding more water in very small increments if needed. Transfer to a floured work surface and knead for 1 minute more. Return to the bowl; cover with a damp cloth.
Divide the dough into 4 pieces and shape each into a square. On a floured surface, roll 1 dough square into a 7-by-10-inch rectangle. Brush the top with 1 1/2 tsp. sesame oil; fold in half. Brush with 1 1/2 tsp. more sesame oil; fold in half again. Repeat with the remaining dough squares.
Roll each dough piece into an 8-by-11-inch rectangle. Distribute the scallions and shrimp lengthwise over half of each rectangle. Fold the other half over the filling; fold in half again. Roll into 9-inch pancakes.
In a skillet, heat 3 tbsp. vegetable oil over medium-high heat. Fry the pancakes 1 at a time, turning once, until golden, 5 minutes. Add more vegetable oil to the skillet as needed. Transfer the pancakes to paper towels to drain. Cut each one into 8 wedges.
In a small bowl, combine the tamari, vinegar, sugar and 1 1/2 tbsp. water. In a medium bowl, toss the lettuce and carrot with the remaining 1 tbsp. vegetable oil and 1 tsp. sesame oil, and 1 tbsp. of the tamari mixture. Serve the pancakes with the salad and the remaining sauce for dipping.