Prep the pan: Heat oven to 350°F (175°C). Line an 8x8-inch pan with parchment, leaving overhang for easy lifting.
Lightly grease the parchment.
Melt chocolate and butter: In a microwave-safe bowl, heat butter and chocolate in 20–30 second bursts, stirring between each, until smooth. Or melt gently over a double boiler.
Whisk in sugars: While the mixture is warm, whisk in granulated and brown sugar until glossy and slightly thick.
Add eggs: Whisk in eggs one at a time until fully blended and shiny. Stir in vanilla.
Stir in yogurt: Fold in Greek yogurt until the batter looks creamy and uniform.
Do not overmix.
Add dry ingredients: Sift in cocoa powder, flour, salt, and a small pinch of baking powder. Gently fold just until no dry spots remain. The batter will be thick.
Optional mix-ins: Fold in a handful of chocolate chips or walnuts for extra texture.
Bake: Spread batter into the pan and smooth the top.
Bake 22–28 minutes, until the edges are set and a toothpick comes out with a few moist crumbs.
Cool and slice: Let the brownies cool in the pan at least 30–45 minutes. Lift out using parchment and cut into squares with a sharp knife, wiping between cuts.