Filling: In a stand mixer or mixing bowl with a hand mixer, combine the softened cream cheese, sugar, egg and vanilla until creamy. Set aside.
Cake Batter: In a mixing bowl, whisk together the flour, baking powder, baking soda, and salt until combined. Set aside.
In a stand mixer or a mixing bowl with a hand mixer, cream together the butter and sugar. Add the eggs to the batter, one at a time. Mix in the vanilla. Alternate adding the flour mixture and the sour cream, mixing to combine.
Spread half of the batter in a 9x13 baking pan that has been sprayed with nonstick spray. Top the batter with the cream cheese mixture. Spread the remaining cake batter over the cream cheese and swirl with a butter knife.
Streusel: In a small bowl, whisk together the sugar and flour. Add the cold, cubed butter and mix into the sugar mixture with a fork or pastry blender until crumbs form. Sprinkle the streusel over the cake batter.
Bake the cake at 350 degrees for 45 minutes or until a toothpick inserted into the center comes out clean.
Glaze: In a small bowl, combine the powdered sugar and milk until smooth. Drizzle over the cake.