Heat oven to 375 degrees F.
Whisk to combine sugar with 1/4 cup water in a small saucepan set over medium heat. Without stirring, cook mixture until dark amber in color, 10 to 12 minutes. Pour 1 tablespoon of caramel into bottom of standard 10 1/2 by 13 1/2-inch muffin tin. Add 1 teaspoon of butter to each muffin cup. Set aside.
Combine cranberries and walnuts in a small bowl. Using a teaspoon, fill apple center with cranberry mixture. Place apples stem side down into caramel.
Meanwhile, on a lightly floured surface, roll out puff pastry to a 12-inch square. Using a 2 1/2-inch cookie cutter cut out 12 circles. Place puff pastry circles over apples, tucking pastry around apples. Bake until puff pastry is golden brown and puffed, 30 to 35 minutes. Turn out immediately onto a baking sheet lined with a silpat nonstick baking mat or parchment paper. Serve immediately.