For the apple puffs: Place the apples in a medium pot with 1/2 cup water, the honey, butter, lemon juice and cinnamon. Stir and cook over medium heat until the apples soften, 10 to 15 minutes. Remove from the heat and stir in the walnuts. Set aside.
Preheat the oven to 350 degrees F and place a rack close to the center of the oven.
On a lightly floured surface, roll the puff pastry to about 1/8-inch thick and cut the pastry into 3-by-3-inch squares. Press the squares into the wells of a mini muffin tin and poke the bottoms with a fork to dock. Place a heaping tablespoon of the apple mixture in the center. Repeat for the remaining pieces of pastry and apple filling.
Bake until the pastries are puffed and golden, 25 to 30 minutes. Transfer the apple puffs to a wire rack to cool while you make the meringue.
For the meringue: In the bowl of a standing mixer fitted with a whisk attachment, beat the sugar, lemon juice and egg whites on medium speed until the meringue is glossy, smooth and holds a stiff peak.
Dollop a tablespoon of the meringue on top of each puff and use a kitchen torch to brown the outside. Alternatively, place the puffs on a baking sheet and broil until the meringue is lightly browned, 2 to 3 minutes. Serve at room temperature.
The apple filling can be made up to 2 days ahead. After cooking, cool the filling, cover and refrigerate until ready to use. The puff pastry can be cut, assembled and kept wrapped and frozen for up to 5 days.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.
Propane gas torches are highly flammable and should be kept away from heat, open flame and prolonged exposure to sunlight. They should be used only in well-ventilated areas. Follow torch manufacturer's instructions for use.