Preheat the oven to 350℉. Grease a loaf pan or cake pan and line the bottom with parchment paper.
In a large bowl, combine the ½ cup plain full-fat yogurt, 1 cup granulated sugar, and 3 large eggs, 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. Add the ½ cup coconut oil and stir well to incorporate. Keep stirring until it forms a smooth batter. Pour and scrape the batter into the prepared pan.
Rest the batter while the oven heats, then place in the oven and bake for 30-40 minutes until a toothpick inserted into the center comes out clean. Do not overbake.
Cool cake on a rack for about 20 minutes; then turn it out of the pan to cool completely.
When the cake is thoroughly cooled, juice the 1 lemon into a bowl and whisk in the sifted ½ cup powdered sugar. Then, evenly spoon the glaze over the top of the cake; it will soak right in.
Notes
Choose your pan. I used a standard-size loaf pan to bake my cake. Other great options include a bundt pan for a prettier final result. This cake also bakes up beautifully in a round 8 or 9-inch cake pan.
What type of yogurt? I prefer a whole milk plain yogurt in this cake. You could also use low-fat yogurt, but I would not use non-fat because you'll lose out on the richness from the higher-fat yogurt. In a pinch, you can try low-fat or regular Greek yogurt.
Add vanilla extract. Add 1 teaspoon of pure vanilla extract to the batter for extra depth of flavor.
Another oil. You can use your choice of oil in this cake. I use melted coconut oil or vegetable oil interchangeably, depending on what I have on hand. But you can use any neutral oil of your choice.
Try another citrus. Swap the lemon glaze for other citrus, like orange or lime.
Skip the glaze. If you want to streamline this recipe even more, omit the glaze, but add citrus zest to the batter as detailed in the tip above. You can use the zest of 1 or 2 lemons, depending on how strong you want the flavor to be.