Preheat oven to 350 degrees F (175 degrees C). Spread walnuts onto a baking sheet.
Toast in preheated oven until nuts start to turn golden brown and become fragrant, 10 to 15 minutes. Coarsely chop walnuts.
Place walnuts in a large bowl. Add whole wheat flour, all-purpose flour, cinnamon, baking soda, salt, and nutmeg; mix until combined.
Mix mashed bananas, honey, eggs, yogurt, coconut oil, butter, and vanilla extract together in another large bowl. Add banana mixture to flour mixture, mixing with a wooden spoon or rubber spatula until batter is just blended.
Grease a 9x5-inch loaf pan. Pour batter into prepared pan.
Bake in the preheated oven until edges and top are golden brown and a toothpick inserted into the center comes out clean, 50 to 60 minutes.
