Because honey keeps baked goods moist, it gives both staying power and flavor to this decadent cake.
Heat oven to 325 degrees with rack in center. Butter an 8-by-8-by-2-inch baking pan. Lightly dust with flour, tapping out excess. Set aside. In a medium bowl, whisk together the flour, salt, and nutmeg, and set aside. In a small bowl, whisk together the eggs and vanilla, and set aside.
In bowl of electric mixer fitted with paddle attachment, beat butter on medium-high until light and fluffy, scraping down sides of bowl as necessary, about 3 minutes. Add sugar and honey; beat mixture until light and fluffy, about 3 minutes.
Add egg mixture a few tablespoons at a time, beating well for 2 to 3 minutes after each addition. Raise speed to high, and beat, scraping down sides of bowl as necessary, until very thick and light in color, 4 to 5 minutes.
Add flour mixture in 3 batches, beating just to combine after each addition. Pour batter into prepared pan.
Bake until a wooden skewer inserted in the center comes out clean, 40 to 50 minutes. Transfer to a wire rack for 5 minutes. Turn cake out of pan and place on the wire rack, right side up, to cool completely.
Transfer cake to serving platter. Using an offset spatula, spread the frosting evenly over the top of the cake.
Frost the cake just before serving. Experiment with using different types of honey. The cake can be made several days in advance; store, covered, at room temperature.