Preheat the oven to 350°F (175°C) and prepare the baking pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In a large mixing bowl, beat the softened cream cheese and butter until smooth.
Gradually add the granulated sugar and continue beating until light and fluffy.
Add the eggs one at a time, ensuring each is fully incorporated before adding the next.
Mix in the lemon zest and lemon juice, then add the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Pour the batter into the prepared pan and smooth the top.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted comes out clean.
Let the cake cool in the pan for 10 minutes, then turn it out onto a wire rack to cool completely.
Dust with powdered sugar before serving, if desired.