Place bacon in a single layer in a lightly greased 13- x 9-inch baking dish; sprinkle with Swiss cheese. Cover; chill up to 8 hours, if desired.
Break eggs over cheese, spacing evenly. Pour whipping cream over eggs; sprinkle with salt and pepper. Bake at 425º for 10 minutes. Sprinkle with Parmesan and paprika. Bake 8 to 10 minutes or until set. Remove from oven; sprinkle with parsley. Let stand 10 minutes before serving.