Lightly butter and flour a 9 by 5-inch loaf pan. Put a rack in the middle of the oven. Preheat the oven to 350 degrees F.
Put the dates in a medium bowl and cover with hot water. Soak for 15 minutes and drain.
In a medium bowl, whisk together both of the flours, baking powder, and salt. Set aside.
In a standing mixer fitted with the paddle attachment, or with an electric hand-held mixer, combine half the dates, butter, and brown sugar and mix on low speed until just incorporated. Raise the speed to high and mix until light and fluffy, about 10 minutes. (Occasionally turn the mixer off, and scrape down the sides of the bowl with a rubber spatula.)
Add the eggs one at time, mixing well after each addition.
Mixing on low speed, add the flour in 3 parts to the butter mixture, alternating with the milk in 2 parts, until just combined. Raise the speed to medium and mix briefly until a smooth batter is formed. Add the remaining dates and walnuts and mix until just incorporated.
Scrape the batter into the prepared pan. Bake, turning the pan halfway through, until golden brown and a toothpick inserted in the center comes out clean, about 1 1/2 hours. Remove from the oven and cool slightly.
Remove the bread from the pan and cool on a rack completely before serving.
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