Preheat the oven to 340 F (170 C). Line an 8-inch baking pan with baking paper, with a little overhang on both sides.
Add water to a saucepan and bring it to a boil. Reduce the heat and let it simmer.
Place the butter and cooking chocolate in a heat-safe bowl and place it in the saucepan with simmering water.
Keep stirring until the chocolate and butter are melted and there are no lumps. Remove the bowl from heat and let it stand for 5 minutes.
Alternatively, microwave the butter and chocolate in 30-second bursts until they are fully melted.
In a separate bowl, combine yogurt and powdered sugar. Whisk well until the sugar melts completely. Take the mixture and rub it with your fingers to check. It should be smooth with no grainy texture.
Add this and vanilla extract to the chocolate-butter mixture.
Sift the flour, cocoa powder, cornstarch, and salt into it.
Mix until the flour is incorporated. Do not overmix, just make sure there are no dry bits of flour.
Pour into the prepared pan and place it in a preheated oven for 25-30 minutes, until a crust is formed. Insert a toothpick to check - it should have moist crumbs.
Cool the brownie in the pan, then place it in the refrigerator for 1-2 hours.
Take the brownie out of the pan by lifting the overhang.
Cut into 16 squares.