Grease a bundt pan or a 9-inch cake pan and line the bottom with parchment paper.
In a small bowl, combine the 1 teaspoon ground cinnamon and 1 tablespoon brown sugar and set aside.
In a large bowl, combine the ½ cup plain full-fat yogurt, 1 cup granulated sugar, 3 large eggs, and ½ cup coconut oil, stirring and whisking until well blended. Add the 1 ¾ cups gluten free flour, 2 teaspoons baking powder, and ¼ teaspoon fine sea salt, mixing just to combine. Gently fold in the 1 cup blueberries.
Add about half of the batter to the prepared pan, then sprinkle it evenly with the cinnamon-sugar mixture, and then top it with the remaining batter.
Preheat the oven to 350℉ and rest the batter while it heats. Then, place in the oven and bake for 35-45 minutes until a toothpick inserted into the center comes out clean. Do not overbake.
Cool the cake in the pan on a rack for about 20 minutes; then gently turn it out of the pan to cool completely.
Notes
Can I use another pan? This cake can be baked in an 8 or 9-inch greased and parchment-lined cake round. You can also try it in a loaf pan. You can layer the cinnamon swirl or simply stir it into the batter. Lots of options!
Use fresh or frozen berries. Fresh berries will give a more intense flavor, but I use frozen blueberries interchangeably. No need to defrost them first! For smaller pops of blueberry, use wild berries, which are a tad smaller.
Skip the swirl. For a simpler, more traditional cake, omit the cinnamon swirl!
Another spice. Swap the cinnamon for ground ginger or cardamom instead of cinnamon for a flavor twist.
Dairy-free: Swap non-dairy yogurt for the yogurt.
Try other additions. Use this gluten free yogurt cake as a base for chocolate chips, other fruit or berries, or nuts.