Line 1 large baking sheet with parchment paper. Place the sheet of puff pastry on a floured surface and cut into 4 even squares. Separate the squares and leave some room between them on the baking sheet. Create a border around the inside of each square by scoring about 1/2-inch around the inside the square. Prick the dough inside the small square. Cover and refrigerate at least 30 minutes and up to 1 day.
Position 1 rack in top third and 1 rack in bottom third of oven and preheat to 400 degrees F.
On each pastry square, overlap slices of apple and nectarine, within the border.
Brush fruit on each tart, with melted butter and sprinkle with 1 teaspoon sugar.
Bake tarts until pastry is golden and apples are tender, about 20 minutes. Drizzle each tart with 1 teaspoon honey. Transfer tarts to racks; cool 5 minutes. Serve warm or at room temperature.
While tarts are cooling, whisk mascarpone with orange liqueur. Top each cooled tart with a dollop of flavored mascarpone.