These tarts look pastry-shop impressive but couldn’t be easier to make! Leaving the skins on the fruit gives them a beautiful rose-like appearance, but if you find the skin tough, feel free to peel the nectarines before you begin.
Preheat the oven to 375 degrees F. Lightly grease a muffin pan with 12 cavities with nonstick spray.
In a medium bowl, toss the sliced nectarines, lemon juice and almond extract if using to combine. In a medium pot, melt the butter over medium heat. Add the sugar and cinnamon and stir until the sugar is completely dissolved. Pour the syrup over the nectarines and toss gently a few times to combine. The heat of the syrup should soften the fruit slightly.
Using flour if necessary, roll out the puff pastry sheets to a 9-by-12-inch rectangle. Cut across the 9-inch side, cutting the dough into six pieces, each 12 inches long and about 1 1/2 inches wide.
Arrange about 10 slices of nectarine along one of the long edges of the dough. Overlap each piece of fruit as you lay them down. Gently fold the excess dough below it up to encase the base of the fruit slices.
Starting from one of the shorter ends, gently roll up the dough and fruit into a spiral and place it, with the skins of the fruit facing up, into the prepared muffin pan.
Bake until the crust is deeply golden brown, 25 to 30 minutes. Cool for 5 minutes inside the pan, then use a small offset spatula to remove the tarts to a cooling rack.
In a small pot, heat the jam over medium heat until it is soft and fluid. Use a pastry brush to generously brush the surface of each tart.