Preheat the oven to 350°F. Line an 9 x 13-inch baking pan with parchment paper on all sides. Set aside.
In a stand mixer fitted with the paddle attachment, combine the melted butter, egg, cake mix, vanilla extract, lemon extract, lemon zest, and lemon juice. Mix together until combined and no streaks of the cake mix remain, about 1 minute.
Use a silicone spatula to scrape the batter into the prepared pan, spreading to the edges and evening out the top. Set aside.
Next, make the gooey lemon layer. In a stand mixer fitted with the paddle attachment (you can just wipe out the bowl you just used!), combine the cream cheese, eggs, powdered sugar, vanilla extract, lemon extract, and lemon zest. Beat on low speed, gradually increasing to medium until smooth and fully combined, about 2 minutes.
Transfer the mixture to the prepared pan, using the silicone spatula to spread the mixture all the way to the edges.
Bake for 35 to 40 minutes or until the edges are light golden brown and the center of the cake jiggles, but feels mostly set (think of it like a cheesecake!). Place the pan on a cooling rack and allow the cake to cool completely in the pan.
Once fully cool, sprinkle with powdered sugar if desired, slice and serve! If not serving right away, store tightly wrapped in the fridge until read to serve!