Step 1

To make the cupcakes, heat the oven to 350°F with a rack in the middle position. Line a 12-cup muffin pan with muffin liners. In a large bowl, whisk together the sugar, flour, cocoa powder, baking soda, baking powder and salt. In a medium bowl or 1-quart liquid measuring cup, whisk together the yogurt, oil, flaxseed meal and vanilla. Add the boiling water and whisk until the mixture thickens slightly, about 1 minute.

Step 2

While whisking, gradually pour the yogurt mixture into the flour mixture and whisk just until smooth. Divide the batter evenly among the cups of the prepared muffin pan. Bake until a toothpick inserted into the center of a cupcake comes out clean, 20 to 25 minutes. Cool in the pan on a wire rack for about 10 minutes, then transfer the cupcakes directly to the rack and cool completely.

Step 3

To make the frosting, in a medium saucepan over medium, bring about 1 inch of water to a simmer. Put the chocolate into a heatproof medium bowl and set the bowl on top of the saucepan; make sure the bottom does not touch the water. Stir occasionally until the chocolate is completely melted. Remove the bowl from the pan and cool to room temperature.

Step 4

In a stand mixer with the paddle attachment, beat the vegan butter and half of the powdered sugar on low until smooth and combined, about 1 minute. Add the remaining powdered sugar, then beat on low until once again smooth and combined, about 30 seconds. Increase to medium and beat the mixture until light and fluffy, 4 to 5 minutes, scraping the bowl once or twice. Add the vanilla and salt, then mix on medium until incorporated, about 30 seconds.

Step 5

Add about 1 cup of the butter mixture to the melted and cooled chocolate and stir with a silicone spatula until well combined. Add the chocolate mixture to the remaining butter mixture in the mixer bowl and beat on low, scraping the bowl as needed, until well combined, about 2 minutes. Mix the frosting by hand, scraping the bottom and sides of the bowl, to ensure it is homogeneous.

Step 6

Top the cooled cupcakes with the frosting, either spreading it with a small icing spatula or piping it on with a pastry bag fitted with a pastry tip. Decorate the cupcakes with candied violet petals (if using).