With the cored side down, make cuts almost all the way through the apples at about 1/4-inch intervals. Leave about 1/8 inch intact at the bottom. Place the apples (cored side down) in the prepared pan.

Melt 1 tablespoon of the butter. Stir in 1 tablespoon of the brown sugar and 1/4 teaspoon of the cinnamon.

Brush the butter mixture over the apples.

Cover the pan with foil. Bake for 20 minutes. Then set the pan on a wire rack to cool for about 10 minutes.

Cut the remaining butter (cold or cool, but not softened) into cubes. Use a pastry blender, a fork, or your fingers to combine the butter, 3 tablespoons brown sugar, flour, 1/2 teaspoon cinnamon, ginger, nutmeg, cardamom, allspice, and salt. Mix in the nuts and oats.

Use two forks or butter knives to fan out the apple sections just a bit. (Nothing too involved; just pull them apart slightly.)

Carefully spoon the topping mixture over the apples, using a small amount at a time. Use a fork or butter knife to push some of the mixture down into the slices.

Bake 15 to 20 minutes, or until the apples are thoroughly baked but not soft. You should feel some resistance when you pierce them, but they should be soft underneath.

Serve warm. Garnish as desired for serving.