Peel and core the apples, leaving them whole. Cut the tops and bottoms off the apples to give them flat surfaces to rest on. In a skillet, melt the butter over medium heat. Stir in the sugar and cook over medium-high heat, stirring, until the mixture begins to turn golden brown and caramelized. Add the brandy and lemon juice and stir to blend. Adjust the heat so the mixture remains at a simmer. Place the apples in the liquid and simmer until the submerged portion is tender, about 15 minutes. Turn the apples over and cook until tender all the way through, about 15 minutes more. Remove from the liquid and set aside to cool.
Preheat the oven to 400 degrees F. Line a sheet pan with parchment or buttered waxed paper. Unroll the puff pastry on a work surface and brush the pastry with melted butter. In a small bowl, toss together the sugar and cinnamon and sprinkle evenly over the pastry. Working lengthwise, cut the pastry into 6 even strips, each 3/4-inch wide. Twist the strips, keeping the cinnamon sugar on the inside, to make long twisted "straws." Transfer to the prepared pan, run your fingers along the twists to straighten, and bake about 20 minutes, until puffed and golden brown.
Pour the sugar into the center of a saucepan. Carefully pour the water around the sugar, trying not to splash any sugar onto the sides of the pan. Do not stir; gently draw your finger through the center of the sugar to moisten it. Over medium heat, bring to a boil without stirring. Cook until light caramel in color and immediately remove from the heat. Carefully (it will bubble up and may splatter) stir in the cream with a wooden spoon until smooth.
To serve, place an apple on each serving plate. Drizzle with caramel sauce, sprinkle with peanuts, and place a pastry straw in the hole of each apple so that it sticks up like a wooden stick.
Recipe courtesy of Gale Gand, “Butter Sugar Flour Eggs” by Gale Gand, Rick Tramonto, Julia Moskin: Clarkson N. Potter Publishers, 1999