Heat oven to 375°. Butter and flour a 9-by-13-inch cake pan. Combine flour, sugar, baking soda, and salt in a large bowl. In a large measuring cup, whisk together eggs, buttermilk, and vanilla.

Melt butter in a small saucepan over low heat. Add cocoa and water, whisking to combine. Increase heat and bring to a boil, whisking occasionally. Pour over flour mixture and stir to combine. Add egg mixture and stir until thoroughly combined.

Pour batter into prepared pan and smooth top. Bake until springy to the touch, about 22 minutes. Transfer cake to a wire rack to cool.

To make glaze, bring butter, buttermilk, and cocoa to a simmer in a small saucepan. Remove from heat and whisk in vanilla and powdered sugar. Let cool slightly before pouring over cooled cake. Decorate with sprinkles, if desired.