Preheat the oven to 325°F. Grease a 9x9-inch baking dish and line with parchment paper.
Melt the butter in the microwave for about 20 seconds. It should be almost fully melted.
Add the butter, sugar, egg, lemon zest, lemon juice, and lemon extract to a large mixing bowl and beat with an electric mixer until creamy.
Add the flour and baking powder to the bowl and mix until combined. Scrape down the sides of the bowl with a rubber spatula and beat for about 2 more minutes until the batter is smooth and fluffy.
Scoop the batter into the prepared baking dish and smooth the top out with a spatula.
Bake for 30 minutes, or until the edges are golden brown and the center is set.
Remove from the oven and allow the bars to cool completely before frosting.
Cream Cheese Frosting
Add the cream cheese, butter, vanilla bean paste, and powdered sugar to a large mixing bowl and beat with an electric mixer until smooth and creamy.
Spread the frosting evenly over the cooled bars and top with extra lemon zest.
Cut into 9 equal-sized squares. Store any leftovers covered in the refrigerator for up to 3 days.