1. MAKE THE FROSTING In a small bowl, stir in the kuzu root starch into the coconut milk until dissolved. In a medium saucepan, whisk the agar into the water and bring to a boil. Simmer over moderately low heat, whisking occasionally, until very thick, 4 minutes. Whisk in the maple syrup, cocoa powder and salt until fully combined. Return to a boil, whisking constantly. Add the kuzu-coconut milk mixture and whisk until smooth. Simmer over moderately low heat, stirring constantly, until very thick and pudding-like, 5 minutes. Remove from the heat and whisk in the chocolate chips, coconut oil and vanilla until the frosting is smooth and glossy. Pour into a glass bowl and let cool to room temperature. Cover with plastic wrap and refrigerate until firm, at least 2 hours or overnight.
2. MAKE THE CUPCAKES Preheat the oven to 350°. Line 16 muffin cups with paper liners. In a large bowl, sift the flour with the baking powder, baking soda and salt.
3. In a food processor, puree the avocado until smooth. In a medium saucepan, whisk the cocoa powder into the coconut milk and cook over moderate heat, whisking constantly, until just beginning to bubble, 2 minutes. Immediately add the cocoa mixture to the food processor along with the maple syrup, coconut oil and vanilla. Puree until smooth, scraping down the side of the bowl once or twice.
4. Scrape the chocolate mixture into the dry ingredients in the bowl and whisk just until combined. Scoop the batter into the lined muffin cups, filling them about two-thirds full. Bake in the center of the oven for about 25 minutes, until a toothpick inserted in the center comes out clean. Let the cupcakes cool in the pans for 15 minutes, then transfer them to a rack to cool completely.
5. Scrape the frosting into a food processor and process until smooth and spreadable. Frost the cupcakes and serve.
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