Preheat the oven to 350°F (175°C). Grease a 9×13 inch baking pan.

For the Cream Cheese Filling: In a mixing bowl, beat together the cream cheese and sugar until smooth. Add in the vanilla extract and egg, mixing well. Set this mixture aside for later.

For the Cake: In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. In another bowl, cream the butter, granulated sugar, eggs, and vanilla extract until smooth. Gradually add the flour mixture to the wet ingredients, alternating with the sour cream. Mix until well blended. Pour half of the cake batter into the prepared baking pan. Evenly spread the cream cheese filling over the batter. Scatter the blueberries over the cream cheese layer. Cover the cream cheese and blueberry layers with the remaining cake batter.

For the Crumb Topping: Using a pastry blender or your fingertips, combine the cold butter, flour, and sugar. The mixture should resemble small peas. Sprinkle this crumb topping over the top of the cake.

Bake in the preheated oven for 55-60 minutes. Check the center with a toothpick to ensure it’s baked through. Important: Do not let the top get too brown, as this can result in an overbaked and dry cake.

Remove from oven, let it cool, then slice and serve.