Cream the softened butter and confectioners' sugar until smooth.

Add the vanilla extract and mix well.

Gradually add the flour at low speed until combined.

Press the dough into an 8x8 inch baking pan.

Refrigerate for about 30 minutes to firm the crust.

Preheat oven to 325 degrees F (165 degrees C).

Prick the dough with a fork and bake for about 30 minutes until golden brown.

Let the crust cool completely.

For the cream cheese filling, cream together the softened cream cheese and granulated sugar until smooth.

Add the eggs and lemon/lime extract and mix until smooth.

Cover the cream cheese filling and refrigerate until ready to use.

For the lime filling, whisk together the egg yolks, cornstarch, and sugar in a non-reactive saucepan.

Whisk in water, salt, and lime juice and bring to a simmer over medium-low heat.

Whisk constantly until the mixture thickens and coats the back of a spoon.

Remove from heat, add lime zest and butter, and stir until smooth.

Let the lime filling cool for 10 minutes.

Reheat the oven to 325 degrees F (165 degrees C).

Spread the cream cheese filling evenly over the cooled crust.

Spread the lime filling evenly over the cream cheese filling.

Bake for 30 to 40 minutes until the edges are light golden brown.

Let cool in the pan on a wire rack to room temperature.

Refrigerate for at least 1 hour or overnight before cutting into 16 squares.

Serve chilled.