Preheat your oven to 350°F (175°C) and prepare an 8x8 inch baking pan by greasing it or lining it with parchment paper.
In a medium mixing bowl, combine the melted butter and granulated sugar. Whisk until smooth, then add the eggs one at a time, mixing thoroughly after each addition. Fold in the vanilla extract.
In a separate bowl, sift together the cocoa powder, all-purpose flour, salt, and baking powder. Gradually incorporate this dry mixture into the wet ingredients, stirring gently until just combined.
In another bowl, beat the softened cream cheese until smooth. Gradually add the powdered sugar, then the Nutella and milk, mixing until creamy and free of lumps.
Pour half of the brownie batter into the prepared baking pan. Add spoonfuls of the cheesecake mixture on top, then pour the remaining brownie batter over it. Dot the top with additional spoonfuls of Nutella.
Using a knife or toothpick, gently swirl the cheesecake and Nutella into the top layer of brownie batter.
Bake for 25-30 minutes. To test for doneness, insert a toothpick into the center; it should come out with a few moist crumbs.
Let the brownies cool in the pan for about 10 minutes, then lift them out using the parchment paper and transfer to a wire rack to cool completely before cutting into squares.
Notes
For an elegant finish, drizzle warmed Nutella over the top and lightly dust with powdered sugar.