In a medium bowl, combine the flour, brown sugar, granulated sugar, and cinnamon. Add the cold, cubed butter and use a pastry cutter or your fingertips to work the butter into the dry ingredients until the mixture becomes crumbly. Place the topping in the refrigerator to chill while you prepare the rest.

In another bowl, beat the softened cream cheese with the sugar until smooth and creamy. Add the egg yolk and vanilla extract, mixing until fully incorporated and silky.

In a large bowl, whisk together the flour, sugar, baking powder, and salt. In a separate small bowl, whisk the milk, egg, melted butter, and vanilla extract. Pour the wet ingredients into the dry ingredients and stir until just combined — be careful not to overmix. Gently fold in the blueberries, ensuring they're evenly distributed without breaking them.

Grease a 9-inch square baking pan and spread the cake batter evenly into the bottom. Dollop the cream cheese mixture on top of the batter, then use a knife or skewer to gently swirl it into the cake. Sprinkle the chilled crumb topping evenly over everything. Bake in a preheated oven at 350°F (175°C) for 40-45 minutes, or until the top is golden and a toothpick inserted into the center comes out mostly clean with just a few moist crumbs.

Allow the cake to cool in the pan for at least 20 minutes on a wire rack before slicing. Serve slightly warm or at room temperature for the best flavor and texture.