Preheat the oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or lightly grease each cup.
Whisk together the whole wheat pastry flour, baking powder, baking soda, ground cinnamon, nutmeg, salt and brown sugar in a large mixing bowl until evenly blended.
In a separate bowl, beat the eggs lightly, then stir in the oil, Greek yogurt, milk and vanilla until smooth and uniform.
Add the wet mixture to the dry ingredients and fold gently with a spatula until just combined — stop when no large streaks of flour remain. Overmixing will make the muffins dense.
Fold the grated apples into the batter until distributed. Let the batter rest for 8–10 minutes at room temperature to allow the whole wheat to hydrate; it will thicken slightly.
Spoon the batter into the prepared muffin cups, filling each about 3/4 full. Smooth the tops lightly with the back of a spoon.
Bake in the preheated oven for 18–22 minutes, rotating the pan halfway through, until the muffins are golden and a toothpick inserted in the center comes out with a few moist crumbs (not wet batter).
Let the muffins cool in the tin for 5 minutes, then transfer them to a wire rack to cool completely. If you like, brush the warm tops with a little melted butter or honey for shine.