Preheat the oven to 350°F. Spray two 8-inch round pans with cooking spray, line with parchment paper rounds, then spray the parchment paper. In a medium bowl, whisk together the gluten-free flour, cocoa powder, baking powder and salt.
In the bowl of a stand mixer, or using a hand mixer, beat together the sugar, eggs, oil, red food dye and vanilla until fully combined, scraping down the bottom and sides of the bowl as needed. Add the sour cream and beat until well-combined.
With the mixer running on low, add ½ of the dry ingredients, followed by ½ of the milk. Mix to combine. Add the remaining ½ dry ingredients and ½ milk, then mix until just combined.
Pour the batter into the prepared pans. Bake for 35-40 minutes, until a toothpick inserted into the center of each cake comes out clean.
Remove the cakes from the oven and let cool in their pans for 15 minutes. Remove each cake from its pan and transfer them to a wire rack to cool completely.
FOR THE CREAM CHEESE FROSTING: In the bowl of a stand mixer, or using a hand mixer, beat the cream cheese, butter and sour cream on medium-high speed until creamy, about 2 minutes.
Add 5 cups of powdered sugar and vanilla and mix on low speed for 30 seconds, then increase to medium-high speed and whip for 2 minutes. Add more powdered sugar if needed to get a thick but spreadable consistency. Frost the cake as desired.