Preheat your oven to 350°F (175°C). Line the bottom and sides of your 9x9-inch baking pan with parchment paper, leaving an overhang on the sides.
Unwrap the Kit Kat bars and place them in a food processor. Pulse until finely crushed.
In a mixing bowl, combine the crushed Kit Kats with 2 tablespoons of softened butter and ½ cup of granulated white sugar. Mix until well combined.
Transfer the crust mixture into the prepared baking pan and firmly press it into an even layer across the bottom. Bake for about 10 minutes, until just set and lightly golden.
In a large mixing bowl, beat the cream cheese until smooth using an electric mixer. Gradually add in the sifted powdered sugar, mixing until creamy.
Add the large egg, freshly squeezed lemon juice, lemon extract, and finely grated lemon zest to the cream cheese mixture. Mix until well incorporated.
Gently fold in the ½ cup of all-purpose flour until just combined.
Pour the lemon filling over the cooled Kit Kat crust, spreading it evenly. Bake for 20-25 minutes, or until the filling is set and the edges are slightly golden.
Once baked, cool completely in the pan. Lift out using the parchment overhang, cut into squares, and serve chilled or at room temperature.