10 tablespoons very soft unsalted butter, plus more for the pan
1⅔ cups granulated sugar
2 large eggs, at room temperature
1 teaspoon pure vanilla extract
½ teaspoon salt
1½ cups plus 2 tablespoons all-purpose flour, plus more for the pan
½ cup plus ⅓ cup unsweetened natural cocoa powder (not Dutch-processed)
1 teaspoon baking soda
1 teaspoon baking powder
1½ cups brewed coffee, cooled to warm
Heat oven to 350º. Generously butter a 9-inch square pan. Line the bottom with parchment, butter the parchment, then flour the bottom and sides of the pan, tapping out any excess flour. This cake is incredibly moist, so I recommend not skipping the parchment.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugar on medium speed until smooth, about 1 minute. Reduce speed to low and add the eggs one at a time, mixing well after each addition. Mix in the vanilla and salt. If mixing by hand, use a wooden spoon to cream the butter and sugar, then switch to a whisk to mix in the eggs. Mix until the batter is smooth and the sugar starts to dissolve.
Sift the dry ingredients directly into the batter, then pour the coffee over. Gently whisk until the dry ingredients are incorporated and the batter is smooth and mostly free of lumps.
Pour batter into prepared pan and tap on the counter to smooth top. Bake until a toothpick inserted in the center comes out with only a few moist crumbs attached, 40-43 minutes.
Place pan on a cooling rack to cool for 20 minutes. Run a knife along the edges of the pan and invert the cake to remove from pan. Turn right side up and cool until just warm.
This cake can be stored, well wrapped in plastic, at room temperature for up to 5 days.