Lightly grease the insert of a slow cooker with oil or cooking spray.
In a mixing bowl, stir together the flour, granulated sugar, cocoa powder, and baking powder until evenly combined.
Add the milk, vegetable oil, and vanilla extract to the dry ingredients. Mix until a thick batter forms.
Spread the batter evenly across the bottom of the prepared slow cooker.
Drop spoonfuls of Nutella over the batter. Use a knife to gently swirl the Nutella into the top layer.
Scatter the chopped hazelnuts across the surface.
Stir the hot water and brown sugar together in a small bowl until the sugar dissolves. Pour this mixture slowly over the cake without stirring it in.
Cover and cook on low for 2 to 2 1/2 hours, until the cake is set on top but a sauce remains underneath. Turn off the slow cooker and let it rest for 10 minutes before serving.