Preheat your oven to 350°F (175°C). Grease your sheet pan with butter or non-stick spray, and set aside.
In a saucepan over medium heat, melt the butter. Once melted, whisk in the unsweetened cocoa powder and brewed coffee until smooth. Remove from heat and let cool slightly.
In a large mixing bowl, whisk together the flour, granulated sugar, baking soda, and salt.
In a separate bowl, mix the eggs, vanilla extract, and Greek yogurt. Once combined, gradually add the slightly cooled chocolate mixture to the wet ingredients, stirring until smooth.
Pour the chocolate mixture into the dry ingredients, and stir until just combined. Be careful not to overmix.
Spread the batter evenly into the prepared sheet pan. Bake in the preheated oven for 20-25 minutes, or until a toothpick inserted into the center comes out clean.
While the cake is baking, prepare the meringue. In a clean mixing bowl, beat the egg whites on medium speed until foamy. Gradually add the superfine sugar, beating until stiff peaks form.
Once the peaks are formed, add the white vinegar and cornstarch, along with the additional cocoa powder. Gently fold to combine.
Once the cake is out of the oven, immediately spread the meringue over the top, ensuring you cover the cake completely.
Return the cake to the oven for an additional 10-15 minutes, or until the meringue is golden brown.
Allow the cake to cool completely before dusting with powdered sugar and slicing. Enjoy your Magic Gooey Chocolate Meringue Texas Sheet Cake with friends and family!