Make the candied almonds by combining 1/2 cup sliced almonds and 2 Tablespoons granulated sugar in a small skillet. Heat over medium-low, stirring constantly, until sugar is completely melted and beginning to brown. Remove from heat immediately and let stand to cool, then break apart.
Make the dressing by combining olive oil, vinegar, parsley, sugar, salt, and pepper in jar with a lid. Seal and shake until sugar is completely dissolved.
Add the chopped romaine to a large salad bowl. Top with shredded chicken, chopped celery, and sliced green onions.
Immediately before serving, add drained mandarin oranges and candied almonds.
Drizzle with dressing as desired.