01 - Preheat the oven to 350°F. Grease and line a 9-inch round cake pan with parchment paper.
02 - Combine cranberries, sugar, water, and orange zest in a small saucepan. Simmer over medium heat, stirring occasionally, until cranberries burst and the mixture thickens, about 5 to 7 minutes. Allow to cool slightly, then mash gently with a fork. Set aside.
03 - In a medium bowl, whisk together the gluten-free flour blend, baking powder, baking soda, and salt.
04 - Using an electric mixer, beat the softened butter and granulated sugar until light and fluffy, approximately 2 to 3 minutes.
05 - Add eggs one at a time to the creamed butter mixture, beating well after each addition. Stir in the vanilla extract.
06 - Add the dry flour mixture to the butter mixture in three parts, alternating with the Greek yogurt, starting and ending with the flour mixture. Mix gently until just combined to avoid overmixing.
07 - Spread half of the batter into the prepared pan. Dollop half of the cranberry mixture over the batter and lightly swirl with a knife. Repeat with the remaining batter and cranberry mixture, swirling again to create a marbled effect.
08 - Bake for 38 to 42 minutes, or until a toothpick inserted into the center comes out clean.
09 - Allow the cake to cool in the pan for 15 minutes, then transfer to a wire rack until completely cool. Dust the top with powdered sugar before serving.