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Preheat the oven to 350 F (175 C). Grease and flour three 8-inch (20-cm) cake pans and set aside (*see the note section for tips if you do not own three pans).
Sift together the flour, cocoa powder, baking powder, baking soda, and salt and set aside .
In a bowl of a stand mixer fitted with a paddle attachment, beat together the oil and sugar on medium speed for 2 minutes. With the mixer on, add the eggs, egg yolk, vanilla, and almond extract. Stop the mixer and scrape down the bowl.
Turn the mixer to low and add the flour mixture in three batches, alternating with the milk, beginning and ending with the flour mixture. Stop the mixer and scrape down the bowl. With the mixer on low, stream in the coffee. Mix on medium-low for no more than 3o seconds, or until combined.
Evenly divide the batter (*see my own notes for tips to do this!) among the prepared pans. Bake for 23 to 25 minutes, or until a toothpick inserted into the center of the cake comes out clean. Let them cool on a wire rack for 10 to 15 minutes before removing the cakes from their pans. Allow to cool completely.
Place the sugar, corn syrup, and 2 tablespoons water in a heavy-bottomed small or medium saucepan. Stir to combine.
Heat over high heat, occasionally swirling the pan, until it turns a medium golden amber color, 8 to 10 minutes. The sugar mixture will begin to rapidly boil before slowing down and darkening in color. Remove the saucepan from the heat once the correct color is reached and the bubbles start to subside.
Slowly and very carefully whisk in the room temperature cream. The mixture will foam up and sputter, so stand clear and keep stirring.
Add the butter and continue to stir until melted. Add the salt and vanilla and stir to combine. Pour the caramel into a heat-safe container and let it cool until it reaches the desired consistency or refrigerate it until ready to use. It will thicken as it cools.
The caramel should be room temperature for cake assembly, but any leftover caramel can be stored in an air-tight glass jar in the refrigerator for up t0 10 days.
Place 1 cup (2 sticks/225 grams) of the butter in a saucepan with the loose tea. Heat over medium heat until the butter melts, then reduce the heat to low and simmer for 5 minutes. Remove from the heat and let the tea steep for 5 minutes more. Strain the butter through a fine-meshed sieve set over a bowl and refrigerate it until it reaches the same consistency as softened butter, 20 to 30 minutes. Small bits of tea may remain in the butter.
Place the egg whites and sugar in the bowl of a stand mixer. Whisk them together by hand to combine. Fill a medium saucepan with a few inches of water and place it over medium-high heat. Place the mixer bowl on top of the saucepan to create a double boiler. The bottom of the bowl should not touch the water. Whisking intermittently, heat the egg mixture until it reaches 160 F (70 C) on a candy thermometer or is hot to the touch. Carefully fit the mixer bowl onto the stand mixer.
With the whisk attachment, beat the egg white mixture on high speed for 8 to 10 minutes, until it holds medium stiff peaks. When done, the outside of the mixer bowl should return to room temperature and no residual heat should be escaping from the meringue out of the top of the bowl. Stop the mixer and swap out the whisk attachment for the paddle.
With the mixer on low speed, add the vanilla, tea infused butter, and remaining 1 cup (225 grams) butter, a couple tablespoons at a time. Once incorporated, turn the mixer to medium high and beat until the buttercream is silky smooth, 3 to 5 minutes.
Once the cakes have completely cooled, level them and choose which layer will be the bottom (tip: pick the sturdiest layer). Place it on a cake plate, turning table, or serving dish. Spread on 1/2 cup (120 ml) of the buttercream with an offset spatula. Top with the next layer of cake and repeat, ending with the third layer (tip: pick a level, attractive layer for the top). Frost the cake with the remaining buttercream and refrigerate it until set, 15 to 20 minutes.
Pour the caramel onto the top of the cake, letting it drip over the edges. Begin by adding 1/2 cup (120 ml) of caramel to the center of the cake and then smooth it out with an offset spatula. Add more caramel as necessary until desired look is achieved.
The cake will keep in the fridge for up to 4 days; it may also be frozen. Store any remaining caramel sauce separately in the fridge for up to 2 weeks.