In a small bowl, combine the flour, sugar, and lemon zest. Add the chilled butter and cut it into the dry ingredients using a fork until the mixture resembles coarse crumbs. Set aside.

Preheat the oven to 350°F (175°C). Position the oven rack in the center. Grease a 9×13-inch baking pan and set aside.

In a large bowl, whisk together the flour, baking powder, baking soda, and salt until evenly combined.

In a stand mixer bowl, beat the softened butter, granulated sugar, and lemon zest until light and fluffy. Add the eggs one at a time, mixing well after each addition. Beat in the vanilla extract.

Reduce the mixer speed to low and gradually add the dry ingredients, mixing just until incorporated. Add the sour cream and mix until smooth. Divide the batter evenly, setting half aside.

Spread half of the batter evenly into the prepared baking pan, smoothing the surface.

In the same mixer bowl, beat the cream cheese, sugar, lemon juice, egg, and vanilla until smooth. Add ¼ cup of the reserved cake batter and mix until fully incorporated. Spoon the filling evenly over the batter in the pan.

Spoon the remaining cake batter over the cream cheese filling. Using a knife, gently swirl the layers together in a figure-eight motion. Sprinkle the streusel topping evenly over the surface.

Bake for 35–40 minutes, or until a toothpick inserted into the cake portion (not the filling) comes out mostly clean. If the toothpick touches the filling, it may appear wet.

Remove the cake from the oven and allow it to cool in the pan on a wire rack for 1 hour. Carefully remove the cake from the pan and continue cooling for an additional 30–60 minutes.

In a small bowl, whisk together the confectioners’ sugar and lemon juice until thick yet pourable. Drizzle over the fully cooled cake and allow the glaze to set before slicing.