Heat the oven to 180°C (350°F). Line an 8 x 8-inch baking pan with parchment paper and set it aside.
Place the chopped chocolate in a microwave-safe bowl and melt in short bursts, stirring between intervals until smooth. Let it rest for 1–2 minutes so it cools slightly.
Whisk the vanilla yogurt, vanilla extract, and sugar into the warm melted chocolate until the mixture is glossy and even. Transfer this mixture to a large mixing bowl.
Add the flour, cocoa powder, and baking soda to the bowl and stir just until combined. Pour in the milk and mix until the batter is smooth and uniform.
If using, gently fold the chocolate chips into the batter until evenly distributed.
Spoon the batter into the prepared pan and smooth the top. Bake for 25–30 minutes, or until a skewer inserted near the center comes out with only a few moist crumbs.
Allow the brownies to cool in the pan for about 10 minutes, then lift them out using the parchment and transfer to a wire rack to cool completely before slicing.