Preheat the oven to 350°. Spray an 8-by-4-inch loaf pan with vegetable oil cooking spray and line it with parchment paper. Spray the paper.
In a medium bowl, whisk the flour with the baking powder and salt. In another medium bowl, combine the melted butter with the cocoa until smooth.
In a food processor, combine the softened butter with the granulated sugar. Add the eggs and vanilla and process until smooth. Add the dry ingredients and pulse just until combined. Add the cream and process until smooth. Transfer 1 cup of the batter to the bowl with the cocoa and stir until smooth.
Spoon half of the remaining batter into the prepared pan and smooth the surface. Spread the chocolate batter in the pan, then cover with the remaining plain batter. Using a table knife, cut 5 swirls in the batter. Bake the pound cake for 25 minutes. Reduce the temperature to 325° and bake for 25 minutes more. Cover loosely with foil and bake for 15 to 20 minutes longer, or until the cake is lightly browned and a toothpick inserted in the center comes out with moist crumbs attached. Let the pound cake cool in the pan for 10 minutes, then unmold and let cool completely on a wire rack. Dust with confectioners’ sugar before serving.
The cake can be wrapped in foil and refrigerated for 1 week or frozen for up to 2 months.