Preheat the oven to 350°F.

Coat an 8x2-inch round cake pan with spray oil.

Line the bottom of the pan with parchment paper and oil the parchment.

Dust the bottom and sides of the pan with 1 tablespoon of the rice flour, shaking out any excess into a medium bowl.

Gently toss blackberries in leftover flour.

Arrange blackberries in a single layer in the pan and drizzle with 2 tablespoons of the maple syrup. Set aside.

Sift together remaining flours, baking powder, baking soda and salt into a large bowl and set aside.

In a medium bowl, beat egg yolks using an electric mixer until light yellow.

Add oil, remaining 1/2 cup syrup and vanilla and beat to combine. Alternately add egg mixture and milk to flour mixture, beating after each addition.

In a separate large bowl, beat together egg whites using an electric mixer until stiff peaks form and gently fold them into batter.

Spoon batter evenly over blackberries, smoothing top.

Bake until top is golden and a knife inserted into the center of cake comes out clean, 40 to 45 minutes.

Cool for 5 minutes, then run a knife around edge of the pan and invert onto a large platter or cake plate.

Peel off the parchment and serve cake warm.