For the cake:
1. Preheat oven to 350 degrees. Grease three 8-inch cake pans with butter and cover the bottom with circles of parchment paper. Grease the parchment and flour the pans. Tap out the excess flour.
2. Mix the cocoa and instant coffee in a small bowl; add the boiling water and mix until smooth. Cool to room temperature, and stir in the yogurt and vanilla.
3. Beat the butter in a bowl with the mixer set at medium-high speed until smooth and shiny, about 30 seconds. Gradually sprinkle in the sugar; beat until mixture is fluffy and almost white, 3 to 5 minutes. Add eggs one at a time, beating 1 full minute after each addition.
4. Whisk flour, baking soda, and salt in medium bowl. With mixer on lowest speed, add 1/3 of dry ingredients to batter, followed immediately by 1/3 of cocoa mixture; mix until ingredients are almost incorporated into the batter. Repeat the process 2 more times. When batter appears blended, stop mixer and scrape bowl sides with rubber spatula. Return mixer to low speed; beat until batter looks satiny; about 15 seconds longer.
5. Divide batter evenly between the three pans. Spread batter to the pan sides and smooth top with a rubber spatula. Bake cakes until a toothpick comes out cleanly, or with just a crumb or two adhering - baking about 18 minutes.
6. Transfer the pans to a wire rack. Cool for 10 minutes and invert to the rack. Peel off the paper liners.
Make the filling:
1. Mix the egg yolks, sugar, salt, butter, cream, and vanilla in a medium, non-reactive saucepan. Cook over a low heat, stirring constantly until mixture is puffy and starts to thicken, 15 to 20 minutes. Pour into a large bowl and stir in the coconut and pecans.
Assemble the cake:
1. Place one of the cakes on the cake plate, cover with the coconut-pecan filling, and repeat for each of the remaining layers. Use the remaining filling to cover the sides of the cake.
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