Place an oven-proof frying pan over medium heat. Add the sugar and heat, shaking the pan occasionally, until the sugar is melted to a deep amber caramel. Add the butter and Baileys and stir vigorously to combine. Arrange the pears, cut side up, in a circular pattern over the caramel and cook for 4-5 minutes until just tender and golden.
While the pears cook, roll out the pastry and cut a disk, roughly 2cm larger than the frying pan. When the pears are nicely coloured on the underside, lay the pastry over the pan, tucking the overhang in around the pears. Transfer the frying pan to the oven and cook for 30-40 minutes until the pastry is puffed and golden brown. Remove from the oven and allow the tarte tatin to sit for 5 minutes. Place a serving plate over the frying pan and carefully turn the tat onto the plate.
Make the custard
In a small saucepan, combine the milk, cream vanilla pod and seeds, and Baileys and heat to just below a simmer.
Meanwhile, in a small bowl whisk together the egg yolks and 1tbs of sugar. Gradually pour the milk mixture into the yolks, whisking well to combine. Return the custard to the saucepan and cook over me low heat, stirring constantly until thickened enough to coat the back of a spoon.
Remove from the heat and immediately pour into a jug Taste, and adjust the sweetness with more sugar if desired. Serve warm or cold alongside the pear tarte tatin.