Preheat the oven to 325°F and place a rack in the center. Line an 8×8-inch pan with parchment paper (leave an overhang on two sides to lift the brownies out after baking).
In a large bowl, whisk together 2/3 cup nonfat vanilla Greek yogurt, 1/4 cup coconut sugar, and 2 large eggs until smooth and well combined.
Place 4 ounces of the dark chocolate and 2 tablespoons coconut oil in a microwave-safe bowl. Microwave in 20–30 second bursts, stirring between bursts, until the chocolate is fully melted and smooth (about 1 minute total). Alternatively, melt gently over a double boiler if preferred.
Whisk the melted chocolate and coconut oil into the yogurt–egg mixture until combined.
In a separate small bowl, whisk together 1/2 cup cocoa powder (42 g), 1 tablespoon cornstarch (9 g), 1/2 teaspoon baking soda, and 1/4 teaspoon salt. Add the dry mixture to the wet ingredients and whisk until just combined and no large streaks remain.
Roughly chop the remaining 1 ounce of dark chocolate and fold it into the batter.
Pour the batter into the prepared 8×8-inch pan and spread it evenly with a spatula.
Bake for about 22–23 minutes, until a toothpick inserted in the center comes out clean. Do not overbake.
Immediately transfer the pan to the refrigerator (placing it on a cooling pad or rack if you like) and chill for 15 minutes to firm. Remove from the fridge and let cool completely at room temperature before using the parchment overhang to lift the brownies from the pan and slice.