Preheat oven to 400°F / 200°C (180°C Fan).
Place the puff pastry sheet onto a parchment-lined baking sheet. Cut the ready-rolled puff pastry into 8 equal rectangles, with each rectangle about 4.5 × 3.5 in (11.5 × 9 cm). Spread the rectangles out a bit so they don’t touch. Score a border (without cutting all the way through) of around 1/2 inch or 1 cm from the edge on each rectangle. Poke a few holes with a fork inside the border.
Halve the apples, remove the core, and slice them into thin slices (about 1/8 inch or 3 mm).
Spread the dulce de leche well inside the border of each puff pastry rectangle. Top each one with overlapping thin apple slices (1/4th apple per tart). If the dulce de leche is too cold or thick and doesn’t spread well, warm it up in the microwave in 15-second increments until it’s spreadable (but not hot).
Place the baking sheet in the oven on the middle rack, and bake until the puff pastry has risen on the sides and is golden around the edges and underneath (about 18-20 minutes). Let the tarts cool for a couple of minutes before the next step.
Warm up the remaining dulce de leche in the microwave in 15-second increments until you can pour it. Drizzle the warm dulce de leche on the baked puff pastry tarts. Serve while warm.