Preheat the oven to 350°F.
In a stand mixer, an electric mixer, or manually, beat the butter and sugar together until creamed and fluffy, for at least 3 minutes.
Add the oil, eggs, yogurt, vanilla, orange zest and beat again to incorporate. Add the almond and rice flours, baking powder, salt, fold until well incorporated. Add ¾ the cranberries and fold again.
Transfer it to your prepared pan. Spread the prepared crumble all over the cake evenly. Sprinkle the remaining cranberries over top.
Bake on the middle rack for about 45-50 minutes, until tested in the center and only a few crumbs (no batter!) come out with it. If the top starts to get to brown, cover it with a piece of parchment or foil. Let the cake cool for at least 30 minutes before slicing. Serve with yogurt or sweetened creme fraiche.