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1. First, combine the peach slices in a bowl with the brown sugar, rum, cinnamon, vanilla and salt. Stir it all together and let the peaches marinate while you get everything else ready.
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2. Preheat the oven to 400 F. Take a sheet tray and line it with either a silicone mat or parchment paper and give it a quick spray with cooking spray.
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3. Lay out the puff pastry sheet on the prepared tray, and score a (1-inch or so) border around the edge of it, pressing lightly with a knife. Within the border, dock the crust all over with a fork to keep it from puffing up, leaving only the border to puff up around the filling.
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4. Arrange the peach slices in rows within the border of the crust along the short side working from the back to the front, letting the next row slightly overlap the previous row.
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5. Bake the easy peach tart for 25 minutes, until the crust is golden and the peaches are soft and tender.
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6. While the tart bakes, prepare a finishing glaze for it. In a small pot combine the water and apricot preserves and heat it over medium heat. Let the mixture simmer and reduce until it is a thick and shiny glaze, about 5 minutes.
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7. Take the tart out of the oven and brush the glaze all over it to make it shiny and glossy. Then let it cool for 10 minutes to set before serving. Cut the tart into the desired sized pieces and serve warm with a scoop of ice cream!
