Step 1: Preheat your oven to 375°F (190°C). Line a 9x13-inch baking pan with parchment paper, leaving an overhang on the sides, and lightly grease the parchment.
Step 2: In a large mixing bowl, cream together the softened unsalted butter and granulated sugar until light and fluffy, about 2-3 minutes with an electric mixer.
Step 3: Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next. Stir in the vanilla extract.
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. You can use your hands or the back of a spoon to spread it out smoothly.
Step 6: Bake for 20-25 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out clean. Do not overbake. Let the bars cool completely in the pan on a wire rack.
Step 7: While the bars cool, prepare the frosting. In a medium bowl, cream together the softened butter, sifted powdered sugar, vanilla extract, and 3 tablespoons of milk until smooth and fluffy. Add more milk, 1 teaspoon at a time, if needed, to reach your desired consistency.
Step 8: Once the sugar cookie bars are completely cool, lift them out of the pan using the parchment paper overhang. Spread the frosting evenly over the top and decorate with sprinkles if desired. Cut into squares and serve.