Place 2 1/4 cups broth in a medium saucepan; bring to a boil. Add rice, stirring well. Cover, reduce heat, and simmer 20 minutes. Remove from heat; let stand, covered, 5 minutes.
While rice cooks, combine remaining 1/4 cup broth, vinegar, and next 5 ingredients in a small bowl; set aside.
Combine rice, peas, and next 3 ingredients in a large bowl. Add vinegar mixture, stirring gently to combine. Cover and chill at least 30 minutes.
Spoon rice mixture onto a lettuce-lined serving plate.