Preheat the oven to 350?F. Grease and flour a 9 x 5 x 3-inch loaf pan with the 1 teaspoon softened butter and 1 tablespoon whole wheat flour.
Combine the remaining 1 1/2 cups whole wheat flour, the all-purpose flour, sugar, salt, baking powder, and baking soda in a large bowl. Whisk to blend. Mix the eggs and beer in a medium bowl and whisk to combine. Stir the beer mixture into the dry mixture until just combined. Pour into the prepared loaf pan. Drizzle the remaining 4 tablespoons melted butter over the top. Bake the bread in the middle of the oven for about 40 minutes, or until a tester comes out clean. Let cool for 5 to 10 minutes in the pan and then turn out onto a rack to cool completely.
Makes one 9-inch loaf