Preheat oven to 350°F. Coat a 9- x 5-inch loaf pan with cooking spray.
Place oats and cashewmilk in a bowl; stir to combine. Let stand 20 minutes.
Whisk applesauce, eggs, maple syrup, brown sugar, oil, and vanilla in a large bowl. Stir in oat mixture. Set aside.
Whisk together flour, apple pie spice, baking powder, salt, and baking soda in a bowl. Add flour mixture to applesauce mixture; whisk just until combined. Pour batter into prepared pan.
For topping, combine oats, brown sugar, and butter in a small bowl. Mix with your fingers until mixture is crumbly. Scatter overtop of bread batter.
Bake at 350°F until a wooden pick inserted in center comes out clean, 50 to 60 minutes. Cool in pan on a wire rack 15 minutes. Remove bread from pan; cool completely. Cut into 12 slices.