Make the Ice Cream. In a large bowl, whisk the cream to firm peaks. Fold in the condensed milk and Baileys and pour into the prepared tin. Freeze for at least 4 hours or ideally overnight.
15 minutes before ready to serve, remove from the freezer and allow to stand at room temperature to soften slightly.
Make the Skillet Cookie. Heat the oven to 180C. Lightly butter the skillet.
In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and sugar and beat until pale and fluffy, scraping down the sides occasionally (about 5 minutes).
Add the egg and vanilla and mix till well combined. Add the Baileys and mix once more until homogenous.
In a separate bowl, sift the flour and baking powder, and gently fold this through the wet mixture. Finally, mix half of each chocolate through the cookie dough and transfer to the prepared skillet, pressing to spread evenly. Scatter over the remaining chocolate and bake in the middle of the oven for 20-25 minutes until risen and golden.
Top the warm cookie with several large scoops of the Baileys ice cream and serve immediately.