Preheat your oven to 350°F (175°C). Grease a 9-inch round cake pan or line it with parchment paper.
Sift together the dry ingredients – In a medium bowl, sift together the all-purpose flour, cocoa powder, baking powder, baking soda, and salt. This ensures there are no lumps and helps to aerate the mixture.
Mix the wet ingredients – In a large mixing bowl, whisk together the sugar, yogurt, vegetable oil, eggs, and vanilla extract until the mixture is smooth and well combined.
Combine the wet and dry ingredients – Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Be careful not to overmix, as this can make the cake tough.
Bake the cake – Pour the batter into the prepared cake pan and smooth the top with a spatula. Bake for about 30-35 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Cool the cake – Allow the cake to cool in the pan for about 10 minutes, then turn it out onto a wire rack to cool completely.
Preparing the Chocolate Ganache:
Heat the cream – In a small saucepan, heat the heavy cream over medium heat until it begins to simmer. Do not let it boil.
Make the ganache – Place the chopped chocolate in a medium bowl. Pour the hot cream over the chocolate and let it sit for a few minutes to soften the chocolate. Then, whisk the mixture until smooth and glossy.
Cool the ganache – Let the ganache cool slightly until it thickens but is still pourable.