Preheat your oven to 350°F and line an 8x8-inch baking pan with parchment paper, leaving some hanging over the sides so you can pull the whole thing out later. Mix the softened butter and granulated sugar together until it's fluffy and light, which takes about 2-3 minutes with an electric mixer. This step is what makes the bars tender, so don't rush it.

Beat in both eggs one at a time, then add the vanilla extract and mix until everything's combined. The mixture should look creamy and smooth at this point. Don't panic if it looks a little separated after the eggs go in—it comes together once you add the dry ingredients.

In a separate bowl, whisk together the flour, baking powder, and salt. Pour the dry mix into your wet ingredients and stir until just combined—don't overmix or your bars get tough. I usually stop mixing when I don't see any white flour streaks, which takes about 30 seconds of stirring.

Pour the batter into your prepared pan and smooth it out into an even layer using the back of a spoon or spatula. Bake for 25-30 minutes until the top's lightly golden and a toothpick inserted in the center comes out clean. Mine usually needs about 28 minutes, but ovens vary, so start checking at the 25-minute mark.

While the bars cool completely in the pan, make your frosting by beating the softened cream cheese with powdered sugar. Add the lemon juice and milk a little bit at a time until you reach a spreadable consistency. The frosting should be thick enough to stay on top but soft enough to spread without tearing the cookie layer.

Once the bars are totally cool (this is important—warm bars will make your frosting melt), spread the frosting over the top in a thin, even layer. Use an offset spatula or the back of a spoon and work quickly so the frosting doesn't crack the bars. I do this about an hour after pulling them from the oven, which gives enough cooling time.

Sprinkle your rainbow sprinkles all over that frosting while it's still soft enough to stick. Let the whole thing set at room temperature for about 15 minutes, then use the parchment paper handles to pull everything out of the pan. Cut into 16 squares using a sharp knife—dipping it in hot water between cuts keeps the frosting from sticking and dragging.