In a small bowl, add in the active dry yeast, 1 teaspoon of sugar and warm milk. Give it a stir and set aside until yeast becomes foamy.
In a large bowl, whisk together egg, melted butter, sugar and salt. Add in the flour and yeast mixture. Switch to a spatula and stir everything together. The dough will be slightly tacky.
Transfer dough to a lightly floured work surface and knead until smooth and elastic. You may need to add additional flour so it isn't too sticky.
Place the dough into a lightly oiled bowl and cover with plastic wrap. Let dough rise in a warm place for about 1 - 1 ½ hours until doubled in size.
Prepare a baking sheet by dusting it with flour. Cut out parchment squares of about 4" by 4" and place them on the baking sheet.
Dust the parchment with a little more flour. It is important to dust with flour so that you don't deflate the dough when you pick it up.
Dust your work surface with flour and roll the risen dough to about ¼" thickness.
Cut out rounds of dough using a 2 ½" round cookie cutter, or you can use mason jar lids as an alternative. Place each dough round onto a floured parchment square. Cover with a tea towel and let the dough rise for another 15-20 minutes, until slightly puffy.
In a medium saucepan over medium heat, pour in oil for deep frying. Heat until the oil reaches 370°F/188°C with an instant-read thermometer.
Carefully (do not deflate dough) pick up parchment square with dough and gently place it into the oil. Fry until golden, about 40 seconds per side.
Remove with a slotted spoon and drain on paper towel. Repeat with the remainder.