Preheat the oven to 350 degrees F. Line an 8-inch square baking pan or 9-inch round cake pan with parchment paper, leaving the sides or tabs overhanging for easy removal. If you don’t have parchment paper, you may simply grease the pan.
In a large bowl whisk together the flour, cocoa powder, baking soda, and salt.
In a microwave safe bowl, heat 1/2 cup of the chocolate chips in 20 second increments, stirring in between until smooth and melted. Stir in the sugar, followed by the yogurt and vanilla.
Half at a time, add the dry ingredients to the wet ingredients. Stir in half of the remaining chips (1/4 cup) and nuts, if using. The batter will be thick.
Spread the batter into the pan, distributing evenly over the bottom. Sprinkle the remaining 1/4 cup chocolate chips over top.
Bake for 25 minutes or until the center is just barely cooked through. (Check a few minutes early as all ovens vary.) Allow the brownies to cool completely. If using parchment paper, the brownies can be easily removed from the pan before cutting. When the brownies are very fresh, cutting will be easier if chilled in the refrigerator for an hour or so.
Cover the brownies or store in an airtight container in a cool, dry place or in the refrigerator. Brownies will maintain freshness for a week or more in the fridge and may be frozen.