FILL a large saucepan with water and add the juice of 1 lemon. PEEL each pear, cut off the top and bottom, then cut into quarters. REMOVE the core and add the pear quarters to the saucepan of lemon water as you go to stop them from browning. PEEL the ginger and smash it with the side of a knife blade but keep intact. DRAIN the pears, reserving 1 cup of the lemon-water for cooking. RETURN the pears to the saucepan with the cup of lemon-water plus the sugar, cinnamon stick and ginger and mix together. BRING to the boil, cover with a lid, reduce the heat to medium and simmer for 20 minutes, stirring halfway through cooking. MIX together the mascarpone, confectioners’ sugar, and vanilla extract in a small bowl. REMOVE the pears and simmer the remaining liquid, uncovered, until it thickens into a syrup. DISCARD the ginger and cinnamon stick and serve the pears drizzled with the syrup and topped with the sweet mascarpone.