Heat oil in a large skillet over medium. Add onions, salt, sugar, and pepper; cook, stirring often, for 5 minutes. Reduce heat to medium-low; cook, stirring often, until onions are golden brown and very tender, about 25 minutes. Stir in sherry, parsley, and thyme; cook, stirring often, until fragrant, about 1 minute. Remove from heat. Stir in 1 3/4 cups of the cheese; set aside.
Preheat oven to 350°F. Place phyllo shells on a baking sheet, and fill each with about 1 tablespoon of the onion mixture; top each cup with some of the remaining cheese. Bake in preheated oven until cheese is melted, about 10 minutes. Place on a serving platter, and sprinkle with chives. Serve hot.