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For the Cake, preheat oven to 350°F. Line an 8-inch square baking pan with parchment paper. Sift flour, sugar, 1 1/2 teaspoons of the baking soda, baking powder and salt into a large bowl or onto a large sheet of parchment paper. Set aside.
In a separate large bowl, mix coconut milk, vegetable oil, 1 tablespoon of the vanilla and applesauce with a wire whisk until well blended. Set aside.
Place aquafaba and cream of tartar in bowl of electric stand mixer fitted with whisk attachment. Beat on high speed until stiff peaks form, about 10 minutes. Gently stir or fold whipped aquafaba mixture into bowl with coconut milk mixture until well blended. Gradually add dry ingredient mixture to batter, stirring gently after each addition just until mixed. Pour batter into prepared pan.
Bake 30 to 35 minutes or until toothpick inserted in center comes out clean. Cool in pan on wire rack 10 minutes. Remove cake from pan and place on large, shallow-sided serving platter. Poke holes in warm cake with kitchen fork at 1-inch intervals, moving fork side to side to enlarge holes slightly.
Meanwhile, mix almond milk, cashew milk, sweetened condensed coconut milk, confectioners’ sugar, cinnamon, remaining 1/4 teaspoon baking soda and 2 teaspoons vanilla in large bowl with wire whisk. Slowly pour milk mixture over cake, reserving about 1/2 cup liquid for serving, if desired. Cool completely. Cover.
Refrigerate at least 3 hours or overnight to allow milk mixture to absorb into cake. Slice and serve with reserved milk mixture drizzled over cake.
To make Sweetened Condensed Coconut Milk, bring 1 can (13.66 ounces) Thai Kitchen® Coconut Milk to boil in a small saucepan; boil 5 minutes. Stir in 1/4 cup agave nectar; reduce heat and simmer 30 to 35 minutes or until the mixture has reduced by half. Set aside and allow to cool completely.
Test Kitchen Tip: Aquafaba is the cooking liquid remaining after cooking legumes, such as garbanzo beans (chickpeas). You can make fresh aquafaba by cooking dried garbanzo beans in water, or simply use the liquid from canned garbanzo beans. Aquafaba is used as an egg replacement. You can whip it like egg whites for meringues or use it as a substitute for whole eggs in baked goods. 3 tablespoons of aquafaba is equivalent to about one egg, while 2 tablespoons of aquafaba is equivalent to about one egg white. One can of garbanzo beans contains about 1/2 cup of aquafaba.