Heat oven to 350°F. Grease a 13x18-inch rimmed sheet pan and line with parchment.
Whisk flour, sugar, baking soda, and kosher salt in a large bowl.
Simmer butter, water, and 1/3 cup cocoa in a saucepan until smooth. Remove from heat.
Pour the warm cocoa mixture over the dry ingredients. Stir until mostly combined.
Whisk eggs, buttermilk, and 1 teaspoon vanilla. Fold into the batter until silky and pourable.
Spread batter in the prepared pan. Bake 18–22 minutes, until the center springs back.
Start the icing near the end of baking: melt 1/2 cup butter with 1/4 cup cocoa and milk; bring just to a simmer.
Off heat, whisk in powdered sugar, 1 teaspoon vanilla, and a pinch of salt until glossy. Stir in pecans.
Pour warm icing over the hot cake and spread quickly. Cool until set, then slice and serve.