Step 1: Preheat your oven to 375°F (190°C). Grease and flour a 9x13 inch baking pan, or line with parchment paper for easy removal.
Step 2: In a large bowl, cream together the softened unsalted butter, granulated sugar, and powdered sugar until light and fluffy, about 2-3 minutes with an electric mixer.
Step 3: Beat in the eggs one at a time, mixing well after each addition. Stir in the vanilla extract. Scrape down the sides of the bowl to ensure everything is fully incorporated.
Step 4: In a separate medium bowl, whisk together the all-purpose flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Step 5: Press the dough evenly into the prepared 9x13 inch baking pan. Use a rubber spatula or lightly floured hands to ensure uniform thickness.
Step 6: Bake for 18-22 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out clean. Avoid overbaking to keep the bars soft and chewy.
Step 7: Let the bars cool completely in the pan on a wire rack before frosting. This is a crucial step to prevent the frosting from melting.
Step 8: For the frosting, in a large bowl, cream together the softened unsalted butter and shortening (if using) until smooth.
Step 9: Gradually add the sifted powdered sugar, one cup at a time, mixing on low speed until incorporated, then increasing speed to medium.
Step 10: Beat in the vanilla extract and milk (or cream), one tablespoon at a time, until the frosting reaches your desired consistency. Beat on medium-high for 2-3 minutes until light and fluffy.
Step 11: Once the bars are completely cool, spread the vanilla buttercream frosting evenly over the top. Decorate with your favorite sprinkles, if desired.
Step 12: Slice into squares and serve. Store any leftover bars in an airtight container at room temperature for up to 3 days, or in the refrigerator for up to a week.