Preheat oven to 350 degrees Fahrenheit. Grease sides and base of springform or round pan.

Combine gluten free flour, baking powder, baking soda, and salt in a bowl large enough to hold all the other ingredients later.

In another bowl, whisk the coconut oil, sugar, and coconut milk together, followed by lemon zest, juice, and vanilla extract.

Pour the liquid ingredients into the bowl of dry ingredients, whisking to combine. Then pour into a prepared pan.

Bake for 30-35 minutes, until the top is golden brown and the sides are shrinking away from the pan. Toothpick should come out clean.

Transfer to a wire rack and remove the cake from the pan, placing on wire rack, after 10 minutes.

Pour blueberries, lemon juice, sugar, and 3 Tbsp of cold water into a saucepan and bring to a boil, then turn down the heat and simmer. Keep stirring gently, for a couple of minutes, until the blueberries have softened in the glossy liquid.

Take the pan off the heat and, in a small cup, mix the cornstarch with 1.5 tsp of cold water. Stir this paste into the pan of blueberries, making sure to scrape the pan clean. 

Stir, put the pan back over the heat, and stir gently for 30 seconds, until bubbling. 

Pour into a container and refrigerate to set.

Do not assemble the cake until just before serving.

Mix the coconut sugar and cornstarch together in a food processor or blender until a fine powder results.

Sift this powdered sugar mixture into the yogurt and stir.

Spread this mixture on top of the cake.

Before serving, gently spoon the blueberry compote on top.