First, make the cookie dough by beating the sugar and butter in a stand mixer or using an electric hand mixer until light and fluffy. Add the vanilla paste and beat again until well combined. Tip in the flour and beat slowly until coming together. Once a dough has formed, tip in the chocolate chips and beat again until all the flour is incorporated, then add the milk and mix until combined. Turn out into a disc, wrap in cling film and leave to chill in the fridge while you make the brownie. If you’re getting ahead, leave in the fridge overnight (maturing it will make the cookie even tastier).
Next, make the brownie. Fill a saucepan a quarter full with hot water and sit a bowl on top so it doesn’t touch the water. Add the chocolate and softened butter and put over a low heat. Stir every now and again until melted evenly.
Remove the bowl from the pan and leave to cool a little. Meanwhile, heat oven to 180C/160C fan/gas 4 and remove the cookie dough from the fridge. Cut off 150g of the cookie dough and set aside for later.
Line the base of your pan with the slightly chilled cookie dough (if making in advance, bring it up to temperature a little before doing this, so it is easier to handle). Press the cookie dough into the base and up the sides of the pan, lining it like a pastry tart case. There’s no need to do this neatly, as once it bakes it will all spread and puff up slightly. Bake in the oven for 15 mins.
While the cookie dough is baking, whisk the eggs and sugar together for the brownie until pale and foamy. Pour the cooled melted chocolate and butter mix over and fold together until well mixed. Finally, fold in the flour until well incorporated.
Remove the cookie base from the oven. Use the back of a spatula or spoon to push it down and back up the sides. Pour over the brownie mixture and return to the oven for 30 mins.
Meanwhile, roll the 150g reserved cookie dough into cherry tomato-sized balls. You should get about 50. Place, a finger-width apart, on a few large baking sheets lined with parchment. In the final 10 mins of the pie baking, bake the cookie balls for 5-8 mins per tray or until golden and cooked through. Set aside to cool.
Remove the pie from the oven and leave to cool in the pan for a few mins before serving. The middle should have a molten, slightly runny centre and the edges should be chewy and crispy. Pile balls of vanilla ice cream in the middle of the pie and top with the mini cookies and a dusting of cocoa powder. Take to the table and dig in.