Butter an 8 or 9-inch round baking pan, line the bottom with a circle of parchment paper, then butter the parchment paper.
In a small bowl whisk together gluten free flour, baking powder, salt, and baking soda.
In a large bowl, using an electric hand mixer, fitted with a paddle attachment, beat together butter and sugar on medium speed until pale and fluffy, 3 to 5 minutes. Beat in the eggs, one at a time, then beat in the vanilla extract.
Scrape down the sides of the bowl, then beat in the yogurt.
Add the dry ingredients on low speed, mixing until just combined. The batter will be thick.
Make the oat crumble: In a medium bowl, whisk together the oat flour, oats, sugar, and salt. Work in the cold butter pieces with your fingers until a clumpy crumble forms.
Spread half of the cake batter into the bottom of the prepared pan and dollop it with half of the lemon curd. Sprinkle about half of the oat crumble evenly over the top and gently swirl the batter. Top with the remaining batter, spreading to the edges. Dollop with the remaining lemon curd and sprinkle with the remaining crumble.
Preheat the oven to 350℉ and rest the batter while it heats. Bake until a toothpick inserted in the cake comes out clean or with just a few moist crumbs and the top is set, about 1 hour. minutes. Remove the cake from the oven and allow it to rest for 30 minutes in the pan on a wire rack before removing the cake.
Run a knife around the inside edge of the pan to loosen the cake from the pan. Place a flat plate over the pan and invert the cake. Peel the parchment round off the cake and gently invert the cake top side up.
Rest the batter. Make sure to rest the cake batter for 20-30 minutes, or at least while the oven heats. This helps the gluten-free batter to hydrate, resulting in a better crumb after being baked.
Add-ins – For a little more flavor, try adding 1 teaspoon of almond extract or 1 teaspoon of ground ginger or cardamom.
Dairy-free - Easily make this cake dairy free by using dairy-free butter and yogurt.
Try oat flour – If you prefer, make this cake just with gluten free oat flour! Instead of a gluten free flour blend, use 1 ¾ cups of oat flour.