Preheat oven to 350 degrees F. Grease a 15x10x1-inch baking pan; set aside.
In a large bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, baking soda, and salt. Beat until combined, scraping bowl occasionally. Beat in eggs, pumpkin, sour cream, milk, and vanilla until combined. Add all-purpose and whole wheat flours; beat until combined. Stir in chopped nuts.
Spread mixture evenly into prepared baking pan. Bake about 25 minutes or until a wooden toothpick inserted near the center comes out clean. Cool in pan on a wire rack.
Prepare Browned Butter Frosting; spread immediately over cooled bars. Cut into bars. If desired, top each bar with a pecan half.
Browned Butter Frosting
In a small saucepan heat 1/4 cup butter over medium-low heat about 8 minutes or until butter turns a light golden brown; cool. In a medium bowl beat the 1/4 cup softened butter with an electric mixer on medium to high speed for 30 seconds. Beat in browned butter until combined. Add powdered sugar, vanilla, nutmeg, and a dash of salt; beat well. Beat in buttermilk to make frosting a spreading consistency. Use immediately. If frosting starts to set up, stir in a small amount of boiling water.