Preheat oven to 350°F (175°C). Line two 9-inch round cake pans with parchment paper and grease the parchment and sides.

Sift flour, cocoa powder, baking soda, baking powder, and salt into a medium bowl; set aside.

In a large bowl, beat room-temperature butter and granulated sugar with an electric mixer on medium speed for 3–4 minutes until pale and fluffy.

Add eggs one at a time, beating 30 seconds after each addition, then mix in vanilla extract just until combined.

On low speed, add one-third of the dry mixture followed by half of the Greek yogurt; repeat, ending with the final third of dry mixture, mixing only until the flour disappears.

Slowly pour in the hot water with the mixer on low, beating until the batter is smooth and slightly thin.

Divide batter evenly between prepared pans, tap to release air bubbles, and bake 32–37 minutes until a toothpick inserted comes out with a few moist crumbs.

Cool cakes in pans 15 minutes, then invert onto a cooling rack and cool completely before frosting.

For frosting, beat butter for 2 minutes until creamy. Sift in cocoa powder and beat 1 minute. Gradually sift in powdered sugar, beating on low; stream in milk, add vanilla and salt, and beat 2–3 minutes until light and fluffy.

Level cooled cake layers if needed. Place first layer on serving plate, spread about 3/4 cup frosting over top, add second layer, and frost top and sides with remaining frosting. Serve or let stand 30 minutes for easier slicing.