In a bowl, combine the mascarpone, sugar, lemon zest and rosemary and mix well. Cover and refrigerate until ready to use.
Put the peaches in a bowl with the lemon juice. Turn to coat, cover and refrigerate for up to one hour.
Preheat a grill pan over medium heat until rim is hot to the touch. Oil the grill pan; place the peach halves on the pan cut side down. Grill until golden brown, about 5 - 6 minutes. Turn them over and cook on the other side.
Remove the peach halves to serving plates. Place a dollop of the cheese mixture on the plate and serve.