Cook the oranges: In a large saucepan, cover the oranges with water. Cover the pan, bring to a boil, then reduce the heat to a simmer and cook the oranges for 45 minutes. Remove the oranges and let them cool for about 15 minutes. Once cooled, cut each orange into 8–12 chunks, leaving the peel on.
Preheat the oven: Preheat to 375°F. Line 1 (9-inch) round cake pan or 2 (8-inch) pans with parchment paper.
Blend the oranges: In a blender, combine the oranges with maple syrup, applesauce, yogurt/milk, and ginger. Blend until the oranges are partially pureed, leaving some small chunks. Set aside.
Mix the dry ingredients: In a medium mixing bowl, stir or whisk together the polenta, almond flour, and baking powder.
Combine and bake: Pour the blended orange mixture into the dry ingredients and stir gently until combined. Pour the batter into the prepared pan(s) and bake 45–55 minutes, or until the edges are dark golden. The top may crack slightly, which is fine.
Cool and serve: Let the cake(s) cool completely in the pan on a cooling rack. Once cooled, remove from the pan(s). Serve with vegan whipped cream and orange slices if desired.
The cake will last 4–5 days in the refrigerator, although it may dry out slightly. It can also be frozen.