Heat oven to 350 degrees and line a muffin pan with 12 baking cups.
Steam squash until tender, about 10 minutes, then transfer to a food processor and puree until smooth.
In a large bowl, whisk together flours, salt, baking soda, baking powder, cinnamon, and ginger. In another bowl, whisk together eggs, 1/2 cup squash puree, sugars, oil, vanilla, and lemon zest.
Fold wet ingredients into dry ingredients until well incorporated, then fold in apple. Spoon batter into baking cups and sprinkle with hazelnuts.
Bake until golden brown and a toothpick inserted in centers comes out clean, about 18 minutes. Transfer to a wire rack to cool.
Combined with grated apple and steamed squash, healthy-fat-rich hazelnut flour ensures a perfectly moist texture in these autumnal treats.