Preheat the oven to 350°F (175°C) and grease and flour a 9-inch round or square cake pan.

In a medium bowl, beat the softened cream cheese with sugar and vanilla extract until smooth. Add the egg and beat until fully combined. Set aside.

In a large bowl, whisk together the flour, sugar, baking powder, and salt.

Add the softened butter, eggs, vanilla extract, and milk. Mix everything together until just combined. The batter should be thick and smooth.

Pour half of the batter into the prepared cake pan, spreading it evenly to cover the bottom.

Spoon the cream cheese mixture on top of the batter, spreading it evenly.

Add the rest of the cake batter on top of the cream cheese layer, spreading it out to cover the filling.

Sprinkle the fresh blueberries evenly over the top of the cake batter.

In a small bowl, mix the sugar, flour, and cinnamon together. Cut the cold butter into small cubes and add it to the dry ingredients. Using a pastry cutter or your fingers, work the butter into the dry ingredients until the mixture forms crumbly bits.

Sprinkle the crumb topping evenly over the cake and blueberries.

Bake in the preheated oven for 45–50 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.