Preheat oven to 375 degrees F (190 degrees C). Grease a 9x5-inch loaf pan. Spread pecans in a single layer on a baking sheet. Bake pecans in the preheated oven until golden, 5 to 7 minutes. Remove pecans from oven and reduce oven temperature to 350 degrees F (175 degrees C). Mix flour, brown sugar, cinnamon, baking soda, baking powder, nutmeg, and salt together in a large bowl. Stir applesauce, water, vegetable oil, and vinegar together in a separate bowl. Stir applesauce mixture into flour mixture until just combined; fold in pecans. Pour batter into the prepared loaf pan. Bake in the preheated oven until a toothpick inserted in the center of the bread comes out clean, 50 to 60 minutes. Cool bread in the pan for 10 minutes before transferring to a wire rack to cool completely.