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 together cake flour, baking powder, and salt in a medium sized bowl. Set aside.
Cream butter, oil, and sugar in the bowl of a stand mixer on medium speed until light and fluffy, about 3 minutes.
Reduce speed to low and add eggs, then egg white one at a time. Mix until incorporated after each addition, scraping down the sides of the bowl as needed.
Add vanilla and mix until just combined.
With the mixer on low speed, alternate adding 1/3 of flour mixture, then 1/2 of the milk, beginning and ending with the flour. Beat between each addition until incorporated. You will have 3 additions of flour and 2 additions of milk. Scrape down the sides of the bowl as needed.
Divide batter evenly between prepared cake pans. Smooth tops with a spatula and tap pans on counter to remove air bubbles.
Bake for 28-32 minutes, or until a toothpick inserted into center of each cake comes out clean.
Remove cakes from oven and let cool in pans for 15 minutes. Remove cakes from pans and let cool completely on a wire rack.
Combine all cherry filling ingredients in a small saucepan over medium heat.
Bring to a boil, then reduce to a simmer. Let simmer for about 10 minutes, stirring frequently, until fruit is soft and starts to break down.
Remove from heat and let cool completely.
Strain cherries through a mesh sieve, reserving juice for buttercream. Set aside.
Preheat oven to 350 degrees Fahrenheit. Set out a small baking sheet.
Combine flour, oats, coconut, sugars, cinnamon, and ginger in a medium mixing bowl.
Add butter cubes and, using your hands (or a pastry blender if you prefer), quickly work the butter into the mixture until distributed and clumps form.
Spread mixture out on baking sheet and bake in preheated oven for 8-10 minutes, or until just golden brown.
Let cool completely. If desired, crumble into smaller pieces.
Add egg whites and granulated sugar to the bowl of a double boiler.** Whisk to combine, then turn on heat to medium.
Whisking frequently, heat the mixture until sugar has dissolved and it registers about 160 degrees Fahrenheit on a candy thermometer. Mixture should feel smooth when rubbed between two fingers.
Pour mixture into bowl of a stand mixer and beat on high speed, using the whisk attachment, until stiff peaks form and the mixture has reached room temperature. This will take 8-10 minutes.
Once cooled, switch to the paddle attachment, then turn mixer to medium-low speed and add butter a tablespoon at a time, beating until incorporated. Then, add vanilla extract and mix just until incorporated.
With mixer on medium-low speed, add some of the juice reserved from the cherry filling one teaspoonful at a time. You want to add the juice gradually to make sure you don't add too much liquid. Your buttercream may be able to handle a little more, or a little less than called for. Beat on medium speed until smooth.
Level your cake layers by using a sharp serrated knife to cut off the rounded domes.
Spread a small amount of buttercream on a cake board, then place bottom cake layer, cut side up, on top.
Pipe a dam of frosting around outer edge of cake layer using a large, round piping tip (this will help keep the filling from spilling out the sides).
Add a layer of cherries in the middle, and sprinkle crisp topping over it, pressing down gently if needed. You can spoon some of the cherry juice in too if you'd like. Then, spread a thin layer of frosting on top of the filling to help stack the next layer.
Stack the second layer of cake, and repeat steps 3 and 4 - pipe a dam of frosting around the edge and fill with the cherries and crisp topping. Add a little more frosting on top.
Stack the third layer, trimmed side down, so the bottom of the cake layer forms the top of the cake.
Frost with a light coat of buttercream to help seal in the crumbs (crumb coat), then chill the cake for about 20 minutes.
Remove from fridge and use remaining buttercream to frost the cake completely. Use an offset spatula or cake scraper to smooth the buttercream.
Decorate as desired. I used a large open star tip to pipe swirls onto the top of my cake, which I then topped with fresh cherries. I sprinkled the remaining crisp topping in the center.
*Make your own cake flour: remove 2 tablespoons per cup of flour and replace it with cornstarch. Sift flour and cornstarch together 4 or 5 times.
**You can also use the bowl of your stand mixer and place it on top of a small sauce pan with a couple inches of simmering water in the bottom. The water should not touch the bottom of the stand mixer.