Preheat the oven to 350 degrees F. Spray a 9x5-inch loaf pan with nonstick spray.
Place the dried dates and water in a small saucepan; heat over medium heat until the water simmers; reduce the heat to low and simmer, 2 minutes. Remove from the heat and set aside.
In a medium bowl, whisk together the flours, walnuts, baking powder, cinnamon, nutmeg, and salt. Make a well in the center.
In another medium bowl, stir together the brown sugar, milk, oil, egg, and vanilla until well blended. Pour into the well of the flour mixture; stir just until combined (do not over-mix), about 1 minute. Pour the batter into the prepared pan.
Bake until a toothpick inserted in the center comes out clean, about 35 minutes. Cool in the pan on a rack, 5-10 minutes, then remove from the pan and place on the rack to finish cooling.