Peheat the oven to 350°F (180°C). Grease and line an 8x8 inch (20x20 cm) pan with parchment paper, leaving an overhang to easily remove the baked cookie slab.
In a mixing bowl, add the granulated sugar and lemon zest and use your finger tips to rub the zest into the sugar to release the lemon oils. Add the softened butter and cream the butter and sugar together on high speed until light and fluffy using a handheld electric mixer. Add the egg, vanilla, salt, and baking powder and mix to combine.
Add the flour and mix until just combined into a thick but slightly sticky dough.
Crumble small pieces of sticky dough evenly across the bottom of the pan and use your fingertips to press the crumbled dough pieces together until they form an even layer.
Bake the sugar cookie bars for around 25 minutes, until they are lightly golden brown around the edges and top.
Remove the pan from the oven and place on a wire rack to cool completely. Once cooled, remove the cookie bar from the pan.
Lemon Buttercream
In the bowl of a stand mixer fitted with the paddle attachment or using an electric whisk, whip the butter, lemon zest and salt until pale and creamy. Add the powdered sugar, and mix on low speed until well combined.
Add a tablespoon of cream and whip on medium-high speed until the frosting is pale and fluffy, scraping down the bowl as needed.
Add the frosting to the cooled cookie bar slap and use an offset spatula to spread it out. Top with sprinkles.
Cut the cookie slab into 16 equal pieces.
Store leftover cookie bars in an airtight container at room temperature for up to 5 days.