For the cake --

2/3 cup all-purpose flour
1/3 cup granulated sugar
2 teaspoons baking powder
1/4 teaspoon kosher salt (heaping)
1/2 cup (1 stick) unsalted butter, melted and cooled slightly
2 eggs
2 tablespoons lemon juice (which was about 1 lemon for me)
1/2 teaspoon vanilla
zest of two lemons

For the cream cheese filling --

8 oz cream cheese, at room temperature
3 tablespoons unsalted butter, melted
1 egg
1 teaspoon lemon extract
1/2 teaspoon vanilla extract
zest of 1/2 lemon
1 cup confectioners' sugar