Preheat the oven to 350°F (175°C). Lightly grease a 9×13-inch (23×33 cm) baking pan.
Whisk together the flour, granulated sugar, brown sugar, and kosher salt in a large mixing bowl. In a medium saucepan, combine the butter, Dutch-process cocoa powder, hot coffee, and water. Cook over medium heat, whisking occasionally, until the butter melts and the mixture reaches a gentle simmer. Continue whisking for about 30 seconds to bloom the cocoa, then remove from the heat.
2 cups (260 g) all-purpose flour, 1½ cups (300 g) granulated sugar, ¼ cup (60 g) packed light brown sugar, 1 tsp (3 g) kosher salt, 1 cup (226 g) unsalted butter, ½ cup (40 g) Dutch-process cocoa powder, ¾ cup (180 ml) hot brewed coffee, ¼ cup (60 ml) water
Pour the hot chocolate mixture over the dry ingredients and whisk until combined, making sure no pockets of dry flour remain. In a separate bowl, whisk together the buttermilk, eggs, baking soda, and vanilla extract. Add to the chocolate batter and whisk until smooth and evenly combined. The batter will be relatively thin and pourable.
½ cup (120 ml) buttermilk, 2 large eggs, 1 tsp (5 g) baking soda, 2 tsps (10 ml) vanilla extract
Pour the batter into the prepared pan and spread evenly. Bake for 25–30 minutes, or until the center springs back lightly when touched and a toothpick inserted into the middle comes out with a few damp cake particles but no wet batter. Because this Texas sheet cake is thicker than the traditional recipe, check the center rather than relying on the appearance of the outer portion of the cake.
Begin preparing the brown butter chocolate frosting during the last 10 minutes of baking so it's warm and ready when the cake comes out of the oven. Melt the butter in a medium saucepan over medium heat. Continue cooking, swirling the pan occasionally, as the butter foams and the milk solids begin turning golden brown. Watch closely once brown specks appear on the bottom of the pan. Remove from the heat when the butter smells toasted and nutty, before the milk solids become dark brown or burn.
¾ cup (170 g) unsalted butter
Immediately whisk the Dutch-process cocoa powder into the browned butter, including the browned milk solids, and stir for about 30 seconds until the cocoa is fully incorporated. Let the mixture cool for 1–2 minutes, then gradually whisk in the buttermilk until smooth and fully incorporated.
⅓ cup (30 g) Dutch-process cocoa powder, ⅓ cup (80 ml) buttermilk
Place the confectioners' sugar and kosher salt in a large mixing bowl, breaking up any lumps. Pour in the warm chocolate mixture, add the vanilla extract, and whisk until the frosting is smooth and thick but still pourable. If necessary, use an immersion blender briefly to smooth out any remaining lumps. The frosting will thicken as it cools, so if it becomes too stiff to pour, whisk in warm water or buttermilk, 1 teaspoon (5 ml) at a time, until it loosens enough to spread. Avoid adding extra confectioners' sugar unless the frosting is unusually thin, since it will continue to firm as it sets.
3¾ cups (450 g) confectioners' sugar, ¾ tsp (2.5 g) kosher salt, 1 tsp (5 ml) vanilla extract
As soon as the cake comes out of the oven, pour the warm chocolate frosting over the hot surface. Use an offset spatula or the back of a spoon to gently spread it across the entire cake, working toward the sides without repeatedly dragging through the frosting. The warmth of the cake helps the frosting spread before it begins to set into a thick fudge-like layer.
Sprinkle with toasted pecans, if using, while the frosting is still soft. Let the cake rest for approximately 20 minutes, or until the frosting has set enough to slice without running. Serve directly from the pan.
¾ cup (100 g) toasted pecans