1/3 cup grated Parmesan cheese
Preheat oven to 350 degrees F (175 degrees C).
Preheat oven broiler; warm oil in a medium skillet over medium heat.
Melt butter in a medium saucepan over medium heat. Saute green onions in butter until light green, then add Parmesan cheese, stirring just until melted. Season with salt and pepper.
Slowly pour soup into vanilla-softened cake pan; let stand 15 minutes. Top each piece of pastry with 1 cup sauce, cutting into wedges; bake 10 minutes, until golden brown. Cool 15 minutes on wire racks.
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