Preheat oven to 350ºF with a rack in middle. Grease a 9-by-5-inch loaf pan (preferably a light-colored metal pan). Place dates and coffee in a heatproof bowl, cover and let stand until dates are softened, about 15 minutes. Drain dates, reserving liquid, and let cool. Whisk flours, cinnamon, baking powder, baking soda and salt.
Using an electric mixer on medium speed, beat butter and sugar, scraping down sides of bowl as needed, until light, about 3 minutes. Add applesauce, eggs, vanilla and reserved liquid from dates until well combined. (Don't worry if mixture looks curdled.) Reduce mixer speed to low and add flour mixture, dates and walnuts until just combined. Spread batter in prepared pan and bake until a cake tester inserted in center comes out with crumbs adhering to it, about 1 hour.
Let cool slightly in pan on a wire rack for 10 minutes, then transfer to rack to cool completely. Cut bread into slices and serve. Wrap leftovers tightly and store at room temperature or freeze.
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