Note: Remember to allow the hard cider to go flat the night before you’re planning to make the muffins, and to cook the kasha ahead of time (see "Buckwheat Pancake Breakfast Muffin" recipe for instructions on how to cook kasha).
The night before baking the muffins, pour the hard cider into an open container and leave out at room temperature to go flat.
Preheat oven to 350°. Place the walnuts in a baking pan and bake until lightly toasted and fragrant, 8 to 10 minutes, shaking the pan midway through baking. Transfer to a plate and let cool, then coarsely chop.
Increase oven temperature to 400°. Generously butter 12 muffin cups and one mini-loaf pan.
In a large bowl, sift the all-purpose flour, buckwheat flour, baking powder, baking soda and salt. Whisk thoroughly, at least 10 seconds, until the dry ingredients are thoroughly blended. Make a well in the center.
In a medium bowl, combine the eggs, oil and maple syrup. Stir in the cider just before you’re ready to combine the wet and dry. (If you add the cider earlier and let it sit, the eggs may curdle slightly.)
Pour the liquid ingredients into the center of the dry ingredients. With a wooden spoon, gently fold the wet and dry ingredients together for no more than 8 or 10 seconds—just until the flour mixture is moistened. There will still be lumps in the batter but that is OK. Gently fold in the kasha and diced apple with a few quick turns.
Using a 1/3-cup measure, fill each muffin well nearly to the top. Pour the remaining batter into the mini-loaf pan and smooth the top.
Bake for 18 minutes or until the muffins are lightly browned and a toothpick inserted into the center comes out clean or with just a few crumbs. Turn the pan halfway through baking.
If the muffin tops have spread, use a plastic knife to cut between them; carefully slide the knife under each muffin top to loosen, if necessary. Remove muffins from the pan and transfer to a cooling rack. Store leftovers in an airtight container lined with a paper towel. Eat within 3 to 4 days, or freeze.