Set the oven rack to the middle position and preheat your oven to 350°F/180°C/160°C fan. Grease two 8-inch round cake pans, set a circle of parchment in the bottom and grease it and a bit of the sides again for extra measure and tap flour in the pan to cover the base and at least ½ inch up the sides.
Whisk together milk, egg whites, and vanilla in an easy to pour from container (I like a medium sized bowl with a pour spout). Using stand mixer with the paddle attachment, mix flour, sugar, baking powder, and salt on low speed until they are combined.
Add 12 tablespoons butter, 1 piece at a time, and mix for about a minute until the largest sized pieces are about pea-sized. Add half of the milky egg white mix and increase speed to medium-high. Beat the batter until it's light and fluffy, this will take another 1 minute or so. Slow the mixer down to medium-low, add remaining milk and egg mixture, and beat until incorporated, about 30 seconds. The batter will look curdled, this is good. Give it a stir by hand for good measure to check the batter's consistency.
Measure ¾ cup (180ml) of batter into two bowls and add and whisk in gel food dye to reach the colour desired. You'll see white flecks in the batter, the final colour of this layer will be the color you see BETWEEN the white flecks, so watch that and don't worry about the white bits.
Pour each batch of coloured batter into its own prepared cake pan. Tilt the pan to cover the whole bottom evenly with batter, give it a wee shoogle (shake) and tap it, level, on the counter once or twice to remove air bubbles. Pop the cake pans in the oven and bake, swapping and rotating them halfway through, until a toothpick inserted in center comes out clean (it's really thin, so go at an angle) or the top has the beginnings of a light golden color, about 10-15 minutes.
Leave the layers to cool in their pans on a cooling rack for 10 minutes. Slip a knife around the edge of each the cake layer and remove them from the pans, peel back the parchment and discard (I used a reusable parchment disc- in that case - wash and dry it for the next layer!). Let the layers cool completely on a cooling rack, they're nice and thin so this won't take long.
Repeat steps 4-6, measuring the batter, dying and baking it, with the remaining batter. You'll get 7 layers.