The honey glaze ensures that this cake is extra-moist.
Preheat oven to 350 degrees with rack in center. Spread walnut halves in a single layer on a rimmed baking sheet. Toast in oven until fragrant, tossing occasionally, 5 to 7 minutes. Transfer nuts to a plate; let cool. Pulse nuts in a food processor until finely chopped, about 10 times. Set aside.
Butter and flour an 8 1/2-inch spring-form pan; set aside. In a large bowl, combine honey and applesauce; whisk until honey is mostly dissolved. Add eggs, and whisk until fully combined.
Into a medium bowl, sift together flour, baking soda, salt, and ginger. Stir into honey mixture. Using a rubber spatula, fold in walnuts.
Pour batter into prepared pan. Bake cake until golden brown on top and a cake tester inserted into center comes out clean, about 55 minutes.
Transfer pan to a wire rack; let cool until sides of cake begin to pull away from pan, about 15 minutes. Remove cake from pan, and place on a serving plate. While cake is still warm, use an offset spatula to gently spread remaining honey on top as a thin glaze. Serve warm.