Preheat the oven to 160°C fan / 180°C conventional. Grease and line the base and sides of three 6-inch cake tins with baking paper.
In a large bowl, cream the butter, white caster sugar, light brown sugar and vanilla extract together until light and fluffy.
Beat in the eggs one at a time until well combined (add 1 tbsp of the 300g flour with each egg to stop the mixture from curdling).
Add the rest of the flour and the milk, then fold together until the cake mixture is smooth and combined.
Divide evenly between the baking tins and scatter the chocolate chips on top of each cake.
Bake for 25-30 minutes until risen, golden in colour and the cakes spring back when lightly pressed in the middle. Leave to cool in the tins for 15 minutes, then turn out onto a wire rack and leave to cool completely.
Make the mini chocolate chip cookies whilst the cakes are cooling:
Cream the butter, white caster sugar and light brown sugar together until light and fluffy. Beat in the egg yolk and vanilla extract. Fold in the flour until the mixture comes together into a cookie dough.
Scoop up teaspoon-sized portions of cookie dough and roll into small balls. Place on a baking sheet lined with baking paper, leaving space between each. Press a few chocolate chips into the top of esch cookies.
Bake for 8 minutes until lightly golden brown and firm around the outside. Leave to cool completely on the baking tray.
Now make the pink vanilla buttercream:
Beat the salted butter until smooth and creamy. Sift in the icing sugar and add the vanilla extract and milk. Beat again until the buttercream is smooth and combined. If it feels a little stiff, add a drop more milk.
Mix in a few drops of pink food colouring to dye the buttercream a baby pink shade.
Assemble and decorate the cake:
Place one sponge layer on a cake stand. Drop two heaped tablespoons of buttercream on top and use a spatula to spread it into an even layer.
Repeat with the second cake layer, then place the third one on top.
TIP: To get a neat and smooth finish, apply a crumb coat by covering the cake with a thin layer of buttercream around the outside and on top. It doesn't have to be super neat and don't worry if you pull up a few crumbs. Place the cake in the fridge to chill for 30 minutes. Now apply a final coat of buttercream, using a spatula or cake scraper to get a smooth finish.
Arrange the cookies around the base of the cake, pressing them gently so they stick to the buttercream.
To finish, use any leftover buttercream to pipe pretty swirls on top and fill in the middle with extra chocolate chips. Slice and enjoy!
Notes
This chocolate chip cookie cake will keep fresh for up to 3 days when stored in an airtight container at room temperature.