For ice-cream, place milk, bay leaves and half the sugar in a saucepan. Bring to a simmer over medium heat, stirring to dissolve sugar. Remove from heat; cool to room temperature (1 hour, see note). Strain mixture into a clean saucepan and stir in cream; bring to a simmer over low heat. Whisk yolks and remaining sugar in a bowl until thick and pale (4-5 minutes); whisk in cream mixture. Return to saucepan and stir continuously over low-medium heat until mixture thickens and coats the back of a wooden spoon (5-6 minutes). Strain into a bowl placed over ice and cool completely. Churn in an ice-cream machine and freeze until required (makes about 1.5 litres).
Place lemon slices in a saucepan, cover with cold water and bring to the boil. Drain. Repeat 4 times until lemon rind is just tender. Carefully remove lemon slices and transfer to a tray lined with baking paper to cool.
Preheat oven to 200°C. Scatter sugar evenly over base of a 22cm diameter cast-iron or stainless-steel frying pan and cook over high heat until sugar begins to dissolve and caramelise around edge (1-2 minutes). Start swirling pan occasionally (do not stir) to caramelise sugar evenly (3-4 minutes). Add butter and swirl to combine (20-30 seconds), then remove from heat and arrange lemon slices, slightly overlapping, in concentric circles over caramel. Cover with puff pastry, tucking edges down around lemons with a spoon. Score centre for steam to escape, then bake until pastry is dark golden and puffed (30-35 minutes).
Remove from oven, stand tart in pan for 2 minutes, then place a plate on top and gently shake pan to loosen tart. Working quickly, invert tart, being very careful of hot caramel drips. Slice and serve hot with bay leaf ice-cream.