In a big bowl, whisk together the milk, sugar, and yeast. Let the mixture stand for 5 to 10 minutes until foamy.
Sift the flour into the milk mixture, add the salt and 1 tablespoon of oil. Mix well with a spatula until the dough starts coming together. Then transfer the dough to a working surface, lightly dusted with flour. Knead the dough for a few minutes until it’s smooth. The dough should be slightly sticky and very soft.
Divide the dough into two equal balls. Lightly brush them oil, then transfer the dough to individual zip lock bags or bowls covered with plastic wrap. Let rest in a warm place (65F-80F) for about 1 to 1 1/2 hrs, or until they are doubled in size.
Place one dough ball on a surface lightly dusted with semolina or flour, then roll it into a large circle, about 1/4 inch thick.
Scoop half of the feta feeling in the center of the dough circle. Fold edges of the dough over the center of the filling and press together to seal, so the filling is no longer visible. Use a rolling pin to gently roll the dough to get a 10-inch circle. Repeat with the remaining dough ball. Be careful not to rip the dough.
Heat a large skillet over medium-high heat. Pour enough oil to completely cover the bottom. Fry the feta flatbreads, one at a time, until golden brown. About 3 minutes per side. Place them on a platter and brush with melted butter. Then cover the bread with a kitchen towel and let steam for about 5 minutes. Serve right away.