In a large bowl, mix together the flour, sugar, baking soda, and salt. Set it aside — that’s your dry base.
In a medium saucepan, melt the butter over medium heat. Once melted, add the cocoa powder and water, whisking until smooth.
Let it just come to a gentle boil, then remove it from the heat.
Pour this hot chocolate mixture straight into your dry ingredients and stir until combined.
In a separate bowl, whisk together the eggs, sour cream, and vanilla extract. Pour that mixture into the chocolate batter and stir until smooth and shiny.
Pour the batter into your prepared sheet pan and spread it evenly with a spatula.
Bake for 20–22 minutes, or until a toothpick inserted in the center comes out clean.
In the same saucepan (no need to wash it), melt the butter over medium heat. Add the cocoa powder and milk, whisking until smooth and slightly bubbly.
Remove from the heat and stir in vanilla extract.
Then, gradually whisk in the powdered sugar until the frosting is silky and pourable.
Once the cake comes out of the oven, don’t wait too long. Pour the warm frosting evenly over the warm cake, letting it spread naturally to the edges.
Let the cake rest at room temperature for about 30 minutes before cutting.