In a large bowl, combine the flour, sugar, salt, and dry yeast.
Add the warm milk, egg, and vanilla extract, then begin to mix the dough until it comes together.
Melt the butter and gradually add it to the dough, kneading continuously until you have a smooth, elastic dough.
Cover the dough with a kitchen towel and let it rise in a warm place for about 1 hour, or until doubled in size.
Meanwhile, prepare the filling: combine the shredded smoked pork with the barbecue sauce and grated cheese.
On a lightly floured surface, roll out the dough to a thickness of about 1.5 cm. Use a large glass or doughnut cutter to cut out circles.
Place a small spoonful of the barbecue pork filling in the center of each dough circle, then place another dough circle on top and press the edges together to seal.
In a deep pot, heat the oil to 350°F (180°C). Test the oil temperature with a small piece of dough – if it immediately rises to the top and gently fries, the oil is ready.
Fry the filled doughnuts for 2-3 minutes on each side, until golden brown.
Remove the fried doughnuts and place them on paper towels to absorb excess oil, then let them cool slightly.
Serve fresh, optionally brushed with extra barbecue sauce on top for an even more flavorful experience!
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