Put 2 cups of the flour, the sugar, yeast and salt in the bowl of a stand mixer fitted with the paddle blade. Stir it once or twice to mix it.
Heat the milk, water and butter over medium-low heat until the butter is melted. Do not let it get hotter than 120 degrees. Cool if needed.
With the mixer on medium speed, slowly pour in the butter and milk mixture. Beat for one minute to mix fully. Add the egg and beat to combine.
On low speed, add the remaining 1 ¾ cups of flour. Beat this until it forms a shaggy dough.
Change the paddle blade out for the dough hook and beat the dough at low to medium low speed for 12-15 minutes. The dough should be smooth and elastic. Add up to one tablespoon more flour if it is too sticky.
Remove the dough and shape into a ball.
Grease large bowl and place the dough in the bowl, turning the dough to make it greasy too. Cover and let rise in a warm place (75-90 degrees) for about 45 minutes until doubled in size.
When risen, punch down the dough and let sit for 5 minutes while you preheat the oven to 375 degrees and prepare the baking sheets by lining them with parchment paper.
Turn the dough out onto a lightly floured board and separate it into 12 equal segments.
Shape each segment in a ball and then flatten the ball to make a 3” circle. Place the circles of dough on the prepared baking sheets, cover and let rise for 15-25 minutes until they have puffed up.
Prepare the Filling
Put all of the filling ingredients together in one bowl and beat until smooth and creamy
Assemble the rolls
Use a small mason jar or glass to press a well in the center of each roll. Fill the well with 2 tablespoons of the feta cheese mixture.
Brush the roll with the egg and water wash.
Bake at 375 degrees for 12 to 13 minutes until the rolls are golden brown and the center of the roll reaches 200 degrees on an instant read thermometer.