Make the cake
Position a rack in the center of the oven and heat the oven to 350°F. Butter a 9-inch cake pan. Line the pan with a piece of parchment paper cut to size.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. In a stand mixer fitted with a paddle attachment or in a large bowl with an electric hand mixer, cream the sugar and butter on medium speed until smooth and fluffy. Reduce the speed to low, add the eggs, and then add the yogurt and vanilla, scraping down the sides of the bowl as needed. Add the dry ingredients and mix until just incorporated.
Transfer the batter to the prepared pan and bake until a toothpick inserted into the center comes out clean, about 45 minutes. Let cool completely on a rack before turning the cake out of the pan.
Make the frosting and frost the cake
Bring the cream to a simmer in a small saucepan over medium heat. Reduce the heat to low, add the chocolate and corn syrup, and whisk until the chocolate is completely melted. Remove from the heat and let cool for 15 minutes. Transfer to a large bowl and refrigerate uncovered, stirring every 30 minutes or so, until it firms to a spreadable texture, about 45 minutes. Transfer the cake to a cake plate. Spread the ganache evenly over the top and sides of the cake with an offset spatula.
Make Ahead Tips
The frosted cake can be refrigerated for up to five days in an airtight cake container (return to room temperature before serving).
Photo: Maren Caruso