Preheat oven to 350 degrees. Spay a 10-inch bundt pan with nonstick cooking spray.
In a medium-sized bowl add flour, baking powder, baking soda, salt, and whisk together with a fork. Using a stand mixer with the paddle attachment beat together the butter and 1 cup plus two tablespoons of sugar, and lemon zest at medium speed until light and fluffy. Add eggs 1 at a time, incorporating into the batter, and adding next egg only after the previous one has been blended. Add 4 teaspoons of vanilla to this mixture.
Reduce speed of mixer to low, add in 1/3 of the dry flour mixture, blend in well, then add about half of the sour cream, blend well, then 1/2 of the dry flour mixture, blend, the remaining sour cream blending in, and then the remaining flour. Pour about 1/2 of this batter into the prepared bundt pan, place the remaining batter into a small bowl, and set aside.
Cream Cheese Mixture: Using the bowl that you mixed the cake batter into add the cream cheese, 5 tablespoons sugar, lemon juice, and 1 teaspoon of vanilla and beat until moist and creamy. Add about 1/4 cup of the batter and mix in well. Spoon this cream cheese batter over the cake batter, spread the mixture towards the center of the pan. You are trying to achieve a nice tunnel, so don't spread this out all the way to the edges. Top with remaining cake batter. Spread cake batter over the top evenly. Bake for approximately 45 to 50 minutes, the cake will be golden. If you are using a cake tester to test the cake, the cream cheese layer will be wet. Cool cake for approximately 1 hour before serving.
Glaze
In a small bowl, combine the powdered sugar and milk until smooth. Drizzle the glaze over the cooled cake.