Thoroughly wash the leeks, then slice them thinly. Peel and finely chop the garlic. Tip: If the leeks are too thick, you can cut them lengthwise to help them cook evenly.
Heat the olive oil in a skillet over medium heat, then add the leeks. Sauté for 5-6 minutes, until softened but not browned. Add the garlic and cook together for another 1-2 minutes.
Pour the heavy cream over the leeks, stir, and cook for 4-5 minutes, until slightly thickened. Then, stir in the grated cheese and season with salt and pepper. Wait until the cheese melts and you get a smooth, creamy consistency.
Let the creamy filling cool completely. This is very important because if you fill the pastry while it's hot, the puff pastry may fall apart or become soggy during baking.
Preheat the oven to 400°F (200°C). Roll out the puff pastry to about 3 mm thick and cut out circles with a diameter of 10-12 cm. Tip: It's a good idea to roll out the dough on a lightly floured surface to prevent it from sticking.
Place 1 tablespoon of filling in the center of each pastry circle. Fold them in half, then press the edges together with a fork to seal well. This will prevent the filling from leaking out during baking.
Place the empanadas on a baking sheet lined with parchment paper. Brush the tops with beaten egg to ensure they bake to a beautiful golden brown. Bake them for 20-25 minutes, until the pastry is crispy and golden brown.
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