Preheat your oven to 350°F (180°C) and line a baking sheet with parchment paper. This prevents sticking and makes cleanup easier.
Melt the white chocolate over a double boiler or in the microwave on low power. Then, mix it with the mascarpone cheese, prosecco, powdered sugar, and vanilla extract. Stir until smooth to create a silky cream.
Lay one sheet of filo pastry on your work surface and brush with melted butter. This helps the layers bake to a crisp and prevents them from drying out.
Spoon 2-3 tablespoons of the prosecco cream onto the center of the sheet and spread it evenly. Gently roll up the sheet lengthwise, being careful not to let the filling squeeze out.
Shape the roll into a spiral (snail shape) and place it on the prepared baking sheet. Repeat the process with the remaining sheets and filling.
Brush the tops with butter to give the burek a beautiful golden and shiny surface. Tip: don't use too much butter, otherwise the end result might be too greasy.
Bake for 30-35 minutes, or until the filo pastry is golden brown and crispy. Keep an eye on it at the end to prevent the white chocolate from caramelizing and becoming too dark.
Let it cool for 10 minutes after removing from the oven, so that the cream slightly firms up and doesn't burn you when slicing. You can sprinkle with a little powdered sugar before serving (optional).
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