Preheat oven to 400º F. In a small bowl, mash together the feta, ricotta, 2 tbsp olive oil, and the oregano. Stir in the mozzarella and garlic. Set aside.
Divide pizza dough in half. Working with one portion at a time, dust dough with flour and roll out ½ -inch thick, dusting with more flour as needed. Cut into 4-inch squares.
Working with a single piece of dough, top with generous tablespoon of feta mixture, top with a second piece of dough and squish slightly to distribute the filling. Cut in half and arrange pieces standing up against one another at one end of greased 9 x 5-inch non-stick loaf pan. Repeat process with remaining dough pieces. Repeat process again with other half of dough.
Cover with a kitchen towel, set in a warm spot and let rise until puffed, 30-45 minutes. Brush top with remaining 2 tbsp olive oil and sprinkle any unused filling over.
Bake for 35-40 minutes or until deeply golden. Let stand for 10 minutes before removing from pan to serve.