Preheat oven to 375°F (190°C).
Remove the core of each apple using a melon baller or paring knife, stopping about half an inch from the bottom to create a well.
In a small mixing bowl, combine the brown sugar, oats, cinnamon, and walnuts.
Mix in the softened butter until the mixture is crumbly.
Divide the stuffing mixture evenly among the apples, pressing it firmly into the cavities.
Place the apples upright in an 8x8 inch baking dish.
Pour the boiling water into the bottom of the baking dish around the apples.
Bake for 40 to 45 minutes, or until the apples are tender when pierced with a knife but still hold their shape.
Remove from oven and baste the apples with the juices from the pan before serving.