Preheat oven to 350°F. Prepare three 8-inch cake pans and two 6 inch round pans with baker's floured cooking spray, or grease and line with parchment rounds.
Mix together all dry ingredients (flour, sugar, baking powder, and salt) in a stand mixer with a paddle until fully combined. Mix bits of room-temperature butter slowly into the dry mix, on a low speed. Continue to mix until no large chunks of butter remain, and the mixture looks crumbly.
Pour in egg whites and mix on low until just incorporated. Mix in the buttermilk and vanilla extract in two installments, on a low speed. Add in and oil, and mix at a low speed until fully incorporated. Scrape down the sides of the bowl with a spatula, then beat on medium speed for about 30 seconds.
Using a kitchen scale, pour 680 grams of batter into each of your 8” pans. Stir lavender extract and purple gel color into the remaining batter, and divide batter evenly between the remaining two 6” pans – I had about 450 grams in each of my smaller pans. (Using the kitchen scale is optional, but guarantees your layers will bake to be the same height.)
Bake for 35-37 minutes, (or until a toothpick or skewer comes out clean). Allow to cool for 10 minutes, then run an offset spatula or knife around perimeter of the pan to separate the cake from the pan, then remove the layers from the pans. Place cake layers into the freezer for 45 minutes, to accelerate the cooling process.
Once the layers have fully cooled, they can be leveled and any caramelized bits can be trimmed from the sides / top of the cake using a serrated knife if desired. Be sure the layers are completely cooled or chilled before trimming. If you try to trim the layers while they’re still warm, they will crumble and break.
While you’re waiting…make your frosting!