Heat oven to 350°F.
Combine all the dry ingredients in a bowl along with the diced butter. Rub the mixture briskly between your fingertips until a loose sandy mixture forms with occasional moist clumps. Refrigerate this mixture while preparing the apples to keep the butter firm.
Cut a small slice off the bottom of each apple to create a flat, stable surface. With a paring knife, cut a cylindrical cone out of the top of the apple, moving about 1 inch outside of the core, similar to removing the top of a pumpkin when carving a jack-o'-lantern. Remove the top and discard.
Using a melon baller or a teaspoon, remove the remaining core and seeds, taking care not to puncture the base of the apple.
Place apples on a baking sheet or pie dish and fill, almost to the top, with honey, about 2 tablespoons per apple. Spoon in oat mixture until full, then pack it down lightly. Add additional mixture until heaped and overflowing over sides of the apples.
Bake on the top or middle rack of the oven until the oat filling is golden brown, about 50 minutes. To check if apples are done, take tongs and squeeze the apples gently. If they give, they are done. Let stand for 10 minutes before serving.