Preheat your oven to 350°F (175°C). Grease your 9-inch round cake pan with butter or non-stick spray and lightly dust with flour. Soften the butter and cream cheese to room temperature.
Beat the softened cream cheese and granulated sugar together until smooth and creamy. Set aside.
Cream together the butter and light brown sugar until light and fluffy, about 3 to 5 minutes. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Alternate adding the self-rising flour and milk (or cream), starting and ending with the flour. Mix just until combined.
Gently fold 1 cup of blueberries into the batter using a spatula, being careful not to break them.
Pour half of the batter into the prepared cake pan and spread evenly. Dollop the cream cheese filling over the batter in spoonfuls, then carefully pour the remaining batter on top, spreading gently. Sprinkle the remaining ½ cup of blueberries over the top.
Bake for 40 to 50 minutes, or until a toothpick inserted into the center comes out mostly clean with a few moist crumbs.
Allow the cake to cool completely in the pan on a wire rack. Dust the top with confectioners' sugar if desired. Slice and serve.