Preheat oven to 350F and grease two 9-inch round cake pans, then line bottoms with parchment paper. Whisk together gluten free flour, sugar, cocoa powder, baking soda, and salt in a large bowl.
Add eggs, buttermilk, vegetable oil, and vanilla extract to the dry ingredients and beat on medium speed for 2 minutes. Slowly pour in hot coffee and stir until the batter is smooth. The batter will be thin, and that is expected.
Divide batter evenly between the two pans. Bake for 30 to 35 minutes until a toothpick inserted in the center comes out clean. Cool in pans for 10 minutes, then turn out onto wire racks to cool completely.
For the frosting, beat softened butter until creamy. Gradually add powdered sugar and cocoa powder, alternating with heavy cream, beating on medium-high until fluffy. Mix in vanilla extract and a pinch of salt.
Place one cake layer on a serving plate, spread a generous layer of frosting on top, then place the second layer on top. Frost the top and sides of the cake.
Slice and serve at room temperature. Store covered for up to 3 days.