For the Cake:

1. Preheat the oven to 350°F (180°C). Grease two 6-inch (15 cm) cake pans with butter and line the bottoms with parchment paper.
2. In a medium bowl, whisk together the flour, cocoa powder, baking soda, and salt. Set aside.
3. In a small measuring cup, combine the buttermilk and red gel food coloring until full combined. Set aside.
4. In the bowl of a stand mixer fitted with a paddle attachment, beat the butter and sugar on medium-high speed for 2-3 minutes until pale and fluffy. Scrape down the bowl halfway through with a silicone spatula.
5. With the mixer running on medium speed, slowly drizzle in the oil. Mix until well combined. 
6. Add the egg and egg yolk one a time, mixing well in between each addition. Scrape down the bowl again and mix in the vinegar and vanilla extract.
7. With the mixer on low speed, add half the buttermilk followed by half of the flour mixture. Repeat with the remaining buttermilk and flour. Mix until just combined.
8. Scrape down the bowl once more to ensure everything is well incorporated. Do not overmix.
9. Transfer the batter evenly into the prepared cake pans and smooth out the tops.
10. Bake for 35-40 minutes or until a cake tester inserted into the center comes out clean. DO NOT open the oven until it’s almost done baking.
11. Let the cakes cool for 5-10 minutes in the pan then invert onto a wire rack. Cool completely before frosting, about 45 minutes. 

For the Ermine Buttercream:

1. In a medium saucepan over medium heat, whisk together the flour, sugar, and salt.
2. Slowly add in the milk while whisking to combine. Continue whisking constantly until the mixture is thick, bubbly, and has a pudding-like consistency, 5-10 minutes.
3. Transfer the mixture to a heatproof bowl and place a sheet of plastic wrap or parchment paper directly over the surface of the roux. This prevents a skin from forming.
4. Cool to room temperature before using, about 2 hours. If making 1-2 days ahead of time, store it in the fridge then bring to room temperature when you’re ready to use it.
5. Once the mixture has cooled, add the softened butter to the bowl of a stand mixer fitted with a paddle attachment.
6. Beat the butter on high speed for 2-3 minutes until pale and creamy. Scrape down the bowl as needed with a silicone spatula.
7. Reduce the speed to medium and add the roux one large spoonful at a time. Mix well between each addition before adding the next spoonful.
8. Scrape down the bowl then add the vanilla bean paste (or extract). Continue mixing until smooth and creamy.
9. Use immediately or store in an airtight container for 1 week. When ready to use, bring the frosting completely back to room temperature then re-whip it in the stand mixer with a whisk attachment.

Assembly:

1. Place one cake layer onto a plate or cake stand, bottom side up. Evenly spread 1/3 of the frosting on top using a small offset spatula.
2. Place the other layer on top, bottom side up. Cover the top and sides with the rest of the frosting and decorate however you like. There should be plenty of buttercream for piping.
3. Chill the cake for 20-30 minutes before serving so it holds up better when slicing. Enjoy!