Preheat the oven to 350°F. Spray an 8x4-inch loaf pan with cooking spray and lightly coat the pan with gluten-free flour. Tap out any excess flour.
In a medium bowl, whisk together the gluten-free flour, baking powder and salt.
Add the sugar, vanilla, eggs and cream cheese to the bowl of a stand or hand mixer. Mix on medium speed for 1-2 minutes until well-combined. Scrape down the bottom and sides of the bowl and mix for another minute.
With the mixer running on low, slowly pour in the melted butter. Continue to mix on low and add the dry ingredients, a little at a time, until fully incorporated. Scrape down the bottom and sides of the bowl and mix again until the batter is completely smooth.
In a small bowl, pour half of the batter and whisk in the cocoa powder until completely smooth.
Add ½ cup of the vanilla batter into the pan, then spread into a thin layer. Add ½ cup of the chocolate batter on top, then spread into a thin layer. Continue to alternate between the vanilla and chocolate batters. Use a knife to make a few large swirls.
Bake for 15 minutes at 350°F, then reduce the oven temperature to 325°F and continue baking for 35-40 minutes. Bake until the cake is golden brown and a toothpick inserted into the center of the cake comes out clean.
Remove from the oven and cool in the pan for 10 minutes. Remove the cake from the pan and transfer to a wire rack to cool completely.