Preheat oven to 350 degrees Fahrenheit. Prepare three 6" cake pans by lining the bottoms with parchment paper, then butter and flour each pan.
Whisk the flour, cocoa powder, instant coffee, baking powder, baking soda, and salt together in a medium size bowl.
In the bowl of a stand mixer, beat the oil and sugars together.
Add the egg and egg yolks one at a time, beating until combined after each addition.
Scrape down the sides and add vanilla. Beat for 30 seconds.
Alternate adding 1/3 of the flour mixture and 1/2 of the buttermilk, starting and ending with the flour. You will have three additions of flour and two additions of buttermilk. Scrape down the sides as needed and mix until incorporated after each addition.
Add the hot water and mix until just combined with a spatula.
Distribute the batter evenly among the three prepared cake pans. Smooth the tops with a spatula and tap gently on the counter to remove air bubbles.
Place cake pans in the oven on the middle rack and bake for 35-38 minutes, or until a toothpick inserted into the center of the cake comes out with just a few moist crumbs attached.
Remove cakes from oven and let cool in pans for about 15 minutes. Then, turn layers out onto a wire rack and let cool completely.
Combine the berries and 1 tablespoon sugar in a small saucepan over medium-low heat, stirring occasionally until juices are released and sugar liquifies.
Stirring frequently, let the mixture simmer for about 10 minutes, until reduced. Use a wooden spoon to help break down the berries as they cook.
Remove from heat and press the puree through a mesh sieve (over a small bowl) to release the juice. Dispose of the seeds and set aside the juice to cool.
Fill the bottom of a double boiler with 1-2 inches of water (water shouldn’t touch the top), then place the egg whites and 2/3 cup sugar in the top bowl. Whisk to combine, then turn heat to medium-low.
Whisking frequently, heat over simmering water until the mixture registers about 160 degrees Fahrenheit on a candy thermometer. When it's ready, the mixture will feel smooth when rubbed between two fingers (i.e. no sugar granules).
Remove from heat and pour the mixture into the bowl of a stand mixer fitted with the whisk attachment. Beat on high speed for 8-10 minutes until stiff peaks form. The meringue should have cooled to room temperature.
Swap out the whisk for the paddle attachment and reduce speed to low. Add the butter, one tablespoon at a time, mixing until incorporated.
Add the vanilla, then gradually add the berry reduction, a tablespoon at a time, mixing to combine after each addition. Be careful to not overwhelm the buttercream with too much liquid. Yours may be able to handle all of the berry puree, or less, depending on how much juice your berries produced.
Beat on medium speed until the buttercream is smooth and fluffy. It may take a few minutes, but keep mixing until it becomes smooth!
Level each cake layer by using a sharp serrated knife to cut off the rounded domes.
Place bottom cake layer on a cake board, using a small amount of buttercream to keep it in place.
Pipe a dam of buttercream around the edge of the cake layer using a large round piping tip.
Spread a thick layer of Nutella in the middle of the buttercream.***
Stack second cake layer on top. and repeat steps 3-4.
Stack third cake layer, bottom side up, on top.
Give the cake a crumb coat of buttercream and place in fridge for about 20 minutes.
Frost additionally as desired.
Top with berries, using extra buttercream to affix to top of cake.
* I make my own buttermilk by adding distilled white vinegar or lemon juice to regular 2% or whole milk. Measure a scan 3/4 cup buttermilk and add 2 teaspoons of lemon juice or vinegar. Stir, and let sit for 5 minutes.
**You can create a double boiler by putting a couple inches of water in the bottom of a small saucepan and placing the bowl of your stand mixer, or another heatproof bowl on top. The water should not touch the bottom of the bowl.
***If Nutella does not spread easily, place it in the microwave for a few seconds at a time, stirring in between, until it reaches a spreadable consistency.