Preheat oven to 350°F. Line a loaf pan with parchment paper.
Make the streusel topping: In a small bowl, combine flour, sugar, and cinnamon. Add walnut butter and stir to coat the flour. Use your hands to pinch the mixture into clumps - if you don't make clumps the streusel will be messy and fall off easily after baking. Place in the fridge while you prepare the bread.
Blend apples: Chop apples and add to a blender or food processor. Blend until you have a chunky applesauce texture.
Combine wet ingredients: Add apples to a large mixing bowl. Stir in vinegar, brown sugar, walnut butter, and vanilla extract. Mix until well combined.
Add dry ingredients: Add whole wheat flour, baking soda, and cinnamon. Fold in with a rubber/silicone spatula until just incorporated and no dry flour is left.
Transfer to loaf pan: Pour the batter into your prepared loaf pan. Sprinkle streusel clumps on top. If you have any leftover apple pieces, you can dice them and add them on top of the streusel.
Bake: Bake for 45-75 minutes depending on loaf pan size. (For a 9-inch pan, start checking the bread around the 45 minute mark. For an 8-inch pan, start checking around 60 minutes. It took me 75 minutes in an 8-inch pan.) Check the bread at the 30 minute mark, and if it's browning too quickly on top loosely tent the bread with aluminum foil. The bread is done when a toothpick/skewer inserted in the center of the bread comes out with no wet batter on it (some crumbs are fine).
Cool: Let the bread cool in the pan for 10 minutes, then remove from the pan, gently remove the parchment paper, and cool the bread on a wire rack. It will take a couple hours for the bread to cool completely.
Storing: Let the bread cool completely, then store in an airtight container. It will keep at room temperature for 1 day. After that, store in the fridge for up to 5 days, or freeze individual slices for up to 3 months.
Notes
Apples: Weigh apples after removing the core. You can peel the apples for a smoother texture, but I usually don't. If you don't have a kitchen scale, you can measure the apples after blending. You need 1 ½ cups blended apples. Gluten-Free Option: Replace whole wheat flour with 120 grams oat flour + 70 grams light buckwheat flour.Streusel: If you like an oat streusel, use 2 tbsp all purpose or oat flour + 2 tbsp rolled oats.