Preheat your oven to 350°F (175°C). Grease a 9x5 inch loaf pan and line it with parchment paper.
Make the cookie crumble by combining the 1/3 cup gluten free flour, 2 tablespoons cocoa powder, brown sugar, and a pinch of salt in a bowl. Rub in the cold butter with your fingertips until coarse crumbs form. Refrigerate while you prepare the batter.
In a medium bowl, whisk together the 2 cups gluten free flour, 3 tablespoons cocoa powder, baking powder, baking soda, and salt.
In a large bowl, beat the softened butter and granulated sugar until fluffy, about 3 minutes. Beat in the eggs one at a time, then mix in the red food coloring, vanilla extract, and white vinegar. Add the buttermilk and stir until combined.
Fold the dry ingredients into the wet ingredients with a spatula until just combined. In a small bowl, mix the cream cheese with the powdered sugar until smooth.
Pour half of the batter into the prepared pan. Drop spoonfuls of the sweetened cream cheese over the batter and use a toothpick to gently swirl it through. Pour the remaining batter on top and smooth it out.
Scatter the chilled cookie crumble evenly over the surface of the bread.
Bake for 55 to 65 minutes, tenting with foil at the 40-minute mark if needed. The bread is done when a toothpick comes out with just a few moist crumbs. Let it cool in the pan for 20 minutes before transferring to a wire rack.