Preheat oven to 350F. Grease/flour or spray a 9 x 13 cake pan. Set aside.
Make the filling: In the bowl of an electric mixer fitted with the paddle, mix together the cream cheese, sugar, egg and vanilla on medium-low speed until creamy. Set aside for the filling. (If you have 1 bowl and paddle, you will need to put this mixture in a separate bowl, and wash them to use to make the cake batter)
Make the cake batter: In medium bowl, stir together flour, baking powder, baking soda and salt until well combined. Set aside.
In the bowl of an electric mixer fitted with the paddle, cream together the butter and sugar on medium-low speed. Add eggs one at a time. Add the vanilla extract. Slowly pour in the flour mixture alternating with the sour cream until it is all combined.
Spread half of the batter into the prepared cake pan with a spatula. Spread the cream cheese filling evenly on top. Top with remaining cake batter and smooth with a spatula. Using a butter knife, gently swirl in the batter.
Make the topping: Add the sugar, flour and chilled butter in a small bowl. Stir using a fork or pastry blender until the mixture is crumbly. Sprinkle the streusel on top of cake batter.
Bake for 40-45 minutes until a cake tester inserted in the center comes out clean. Cool on a rack.
To make the glaze: In a small bowl, combine confectioners’ sugar and milk until creamy. Drizzle over cake.