Preheat oven to 400 degrees F. In a medium ovenproof skillet melt butter over medium heat. Stir in shallots and honey. Cook 10 minutes or until shallots start to brown, stirring occasionally. Stir in balsamic vinegar, salt, and pepper.
Transfer skillet to oven. Bake 15 to 20 minutes or until shallots are tender and liquid is syrupy.
Meanwhile, on a large baking sheet unfold puff pastry. Trim a 1/2-inch-wide strip from each side of the pastry. Combine egg yolk and water. Lightly brush edges of the pastry sheet with egg yolk mixture. Place the pastry strips on the edges of the pastry sheet to form a ridge, trimming any excess pastry. Lightly brush ridge with egg yolk mixture. Using a fork, generously prick bottom of pastry.
Bake 15 to 20 minutes or until pastry is puffed and golden brown. Spread shallot mixture over bottom of pastry. (Pastry will sink when topped with the shallot mixture.) Top with cheese. Bake 3 to 5 minutes more or until cheese is softened.
Transfer tart to a wire rack. Sprinkle with parsley. Let stand 5 minutes before serving.