Combine vinegar and mustard in a small bowl, stirring with a whisk. Add oil, 1/8 teaspoon salt, sugar, and black pepper, stirring with a whisk until blended.
Combine water and remaining 1 teaspoon salt in a large Dutch oven; bring to a boil. Add shrimp; cook 3 minutes or until done. Drain and rinse with cold water; finely chop. Combine shrimp, parsley, and chopped onion in a medium bowl; stir in 4 teaspoons vinegar mixture. Gently fill each piquillo pepper with about 1 1/2 tablespoons shrimp mixture.
Place endive, watercress, and sliced onion on a large platter, tossing to combine. Top with stuffed peppers, and drizzle with remaining vinegar mixture.