Preheat oven to 400°F. Line a baking sheet with a sil-pat or parchment paper.

Make the Rosemary-Lime Sugar: In a medium mixing bowl, add the sugar, salt, lime zest and the rosemary leaves. With your fingertips, mix it all together, rubbing it gently until it’s combined and fragrant. Set aside.

On a lightly floured surface, unfold puff pastry and, using a rolling pin, gently roll it into a 15 x 12 inch rectangle. Cut it into 4 squares. Transfer to the lined baking sheet. With a sharp knife, using gentle pressure, score a border about 1-inch from the edges, but don’t cut all the way through the dough. Inside the rectangles, poke dough all over with a fork. (Dough should be as cold as possible when you bake it so refrigerate until the apples are ready).

Layer the apple slices in two rows, overlapping them slightly, leaving the border edge bare. Sprinkle with the rosemary-lime sugar, then dot the surface with butter cubes. Bake for 25-30 minutes, until the pastry is golden brown and the edges of the apples start to brown. Let cool for at least 15 minutes.

If you want the tarts to look shiny and glazed, add apricot jelly into a small dish and thin with 1 tablespoon hot water, then brush glaze lightly over the apples.