1/2 cup adzuki beans
1 1/2 cups water
1/4 cup brown sugar
3 cups sweet white rice flour
2 tsp baking soda
1/4 tsp salt
1/2 cup butter, soft
1 cup sugar
2 tsp orange zest
3 tbsp ground flaxseed + 6 Tbsp hot water
2 cups unsweetened soy milk
1 cup powdered sugar
3 Tbsp fresh orange juice
Sort and rinse beans. Place in a pot of water. Cover and bring to a boil. Reduce heat to medium-low and simmer until soft, about 1 hour. Drain beans, reserving cooking liquid.
Place beans and brown sugar in a food processor and pureé, adding reserved cooking liquid 1 tsp at a time until mixture is smooth. Set aside.
Preheat oven to 350 F. Line a 9x13-in cake pan with parchment paper. In a small bowl, combine flour, baking soda, and salt and set aside.
Cream butter and sugar until fluffy. Add orange zest and flaxseed. Add the dry ingredients, alternating with the milk, until batter is smooth.
Mix 1/2 cup batter with bean pureé. Pour remaining batter into cake pan and smooth top. Drop dollops of bean purée on top. Run a butter knife through the bean purée, creating swirls.
Bake until a toothpick inserted in the center comes out clean, about 45 minutes. Let cool completely before icing. For icing, whisk together powdered sugar and orange juice until smooth. Drizzle and smooth over the cake. Let set before serving.