Peel and deseed the pumpkin, then dice it into small cubes. Tip: If it's hard to peel, microwave for 1-2 minutes to soften it slightly.
Heat 1 tablespoon of olive oil in a medium skillet over medium heat. Add the minced garlic and sauté for 1 minute until fragrant. Add the diced pumpkin, season with salt and pepper, and cook for 10-12 minutes, or until tender.
Stir in the crumbled feta cheese and finely chopped fresh basil into the cooked pumpkin. Mix well and let it cool slightly. The filling should be creamy and well-combined.
Preheat your oven to 350°F (180°C). Line a baking sheet with parchment paper or grease it lightly with olive oil.
Lay out one sheet of filo pastry, brush it with olive oil, and top with another sheet. Spread the filling lengthwise along one edge of the pastry, then roll it up into a burek shape – either a spiral or a log. Repeat until all the filling and pastry are used.
Place the bureks on the prepared baking sheet, brush the tops with olive oil, and bake for 25-30 minutes, or until golden brown. Tip: If they brown too quickly, cover them loosely with parchment paper.
Once baked, let the bureks rest for 5-10 minutes before slicing and serving warm.
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