Preheat the oven to 180°C (350°F). Line an 8 x 8-inch baking pan with parchment paper and set aside.
Place the chopped chocolate in a microwave-safe bowl and microwave in short bursts, stirring between, until melted and smooth. Let sit 1–2 minutes.
Add the vanilla yogurt and sugar to the melted chocolate and whisk until fully combined and smooth, then transfer the mixture to a large mixing bowl.
Add the flour, cocoa powder, and baking soda to the bowl and stir until just combined.
Stir in the milk until the batter is smooth and fully incorporated.
Fold in the chocolate chips, if using.
Pour the batter into the prepared pan and spread it evenly.
Bake for 25–30 minutes, or until a skewer inserted in the center comes out just clean.
Remove from the oven and cool in the pan for 10 minutes, then transfer to a wire rack to cool completely before slicing into 12 brownies.