Whisk balsamic vinegar, Dijon mustard, brown sugar, garlic, salt, and pepper together in a bowl until mixed. Stream olive oil into the vinegar mixture, whisking until smoothly incorporated.
Pile romaine in a mound on a large platter. Arrange strawberries, mango, and jicama atop the lettuce. Combine barley, celery, and pecans in a bowl; sprinkle over the salad. Serve with the vinaigrette.
