First, make the sheet cake. Position a rack in the center of the oven and preheat the oven to 350°F. Lightly spray a 9 x 13-inch sheet pan with cooking spray.
Mix the dry ingredients. In a small bowl, whisk together the flour, sugar, and salt.
Melt the butter, then add the cocoa, water, and dry ingredients. In a medium, heavy-bottomed saucepan, melt the butter over medium-low heat. Once the butter has melted, add the cocoa powder and water, mixing together with a heatproof rubber spatula to combine. Bring to a boil over medium-high heat and boil for 30 seconds.Remove from the heat and place on a wire rack. Immediately add the dry ingredients and mix until smooth. Allow to cool slightly while you prep the rest of the ingredients. Whisk the buttermilk, egg, vanilla, and baking soda, then add to the cocoa mixture. In a small bowl, whisk together the buttermilk, egg, and vanilla until combined. Whisk in the baking soda, then immediately add the entire mixture to the cocoa mixture in the saucepan and mix until just combined.
Assemble the cake for baking. Pour the batter into the prepared pan. Pick up the pan and tilt it from side to side to spread the batter into a thin, even layer across the pan.
Bake the cake. Bake for 20 to 22 minutes, or until the top of the cake bounces back when gently pressed and a skewer inserted into the center of the cake comes out with a few crumbs attached.
Meanwhile, toast the pecans for the frosting. Spread the pecans in a single layer across a medium frying pan. Cook over medium heat for 5 to 10 minutes, using a heatproof rubber spatula to toss the nuts every 2 to 3 minutes, until fragrant and brown. Once toasted, scrape the nuts onto a plate fo prevent them from cooking further.
Make the frosting. In another medium, heavy-bottomed saucepan, melt the butter for the frosting over medium-low heat. Once the butter has melted, add the cocoa powder for the frosting, whisking together to combine. Once combined, add the milk, vanilla, confectioners' sugar, and salt. Continue to cook over very low heat, whisking continuously, until no lumps from the confectioners' sugar remain and the frosting is very smooth, about 5 minutes. At this point, the cake should be done baking.
Assemble the cake. Place the warm cake on a wire rack for assembly. Add the pecans to the frosting and mix to combine, then pour over the warm cake. Immediately pick up the pan (be careful—it will still be hot, so use oven mitts!) and tilt it from side to side to spread the frosting into a thick, even layer across the cake. Cool the assembled cake on the wire rack for 1 hour, or until the frosting has set and feels solid when gently pressed. Serve and store. Serve at room temperature. The Texas sheet cake will keep, covered tightly in plastic wrap, at room temperature for up to 3 days.