To Make the Cake: Heat oven to 325 degrees F. Oil four 8" round cake pans and line the bottoms with parchment; oil the parchment. In a medium bowl, whisk together flour, baking powder, and salt.
Using an electric mixer, beat butter and sugar in a large bowl on high speed until light and fluffy, about 3 minutes. Reduce speed to medium and add eggs, one at a time, beating each egg until fully incorporated before adding the next egg. Add the vanilla extract.
Reduce speed to low and add the flour mixture in three parts, alternating with the milk and beating just until incorporated.
Once the batter is ready, add a drop or two of the pink for a really light pink hue. Then remove 2 1/2 cups of batter from the main bowl and put it into the first prepared cake pan. Next, add another couple of drops of food coloring to the batter in the mixer to create the next color layer and then transfer another 2-1/2 cups into the next prepared pan. Repeat this process two more times to create four increasingly deeper colored layers. Alternatively, you can divide the batter among four bowls (2-1/2 cups in each bowl) and make your colors from there.
Pick up and drop the pans onto the counter from about 6 -8 inches in the air to remove bubbles.
Bake until a wooden pick inserted into the center comes out clean, 30 to 35 minutes. Transfer cakes to a wire rack and let cool in the pans for 10 minutes, then invert each onto the rack to cool completely.
Using a serrated knife, trim the rounded tops of all the cakes to make flat, even layers. If the sides of the cakes are dark, freeze for 2 hours, then gently file the edges using a Microplane or small-holed grater to reveal the true cake color.
To Make the Frosting: Sift confectioners' sugar into a bowl. Using an electric mixer, beat butter in a large bowl on medium speed until creamy, about 2 minutes.
Reduce speed to low and gradually add the sugar, alternating with the heavy cream. Beat in the vanilla extract. Increase speed to high and beat until fluffy, about 2 minutes.
To Assemble the Cake: Place the deepest pink cake on a cake stand and top with a heaping 1 1⁄2 cups of the buttercream, spreading evenly just to the edges. Sandwich with the second- deepest pink cake. Repeat layering, using the other cake layers to create an ombré effect. Finish with a layer of frosting. To prevent drying, cover cake with plastic wrap until ready to serve.
Notes
Make Ahead: The baked cake layers can be frozen for up to one week.