1. Make the pita: In a small bowl, combine the sugar, yeast, warm milk, and warm water. (The milk and water should be warm to the touch but not hot, about 105-110°F. You can check with a meat thermometer.) Let sit for 5 minutes until frothy, then mix in the olive oil.
2. In a large bowl, whisk together the flour and salt. Add the yeast mixture and mix until a shaggy dough forms.
3. Knead on a lightly floured surface for 4-5 minutes until smooth and elastic, then place the dough in a lightly oiled bowl, cover, and let rise for 45 minutes or until doubled in size.
4. Transfer the dough to an oiled surface and divide it into 6 equal pieces. Using your fingers, gently press and spread each piece into a 1/4-inch-thick circle on the oiled surface.
5. Make the garlic butter: In a small bowl, combine the butter and garlic and microwave until melted (or melt them together in a pan), then stir in the chopped parsley.
6. Heat a lightly oiled medium skillet over medium heat. Cook each pita for about 2 mins per side, until puffed and golden.
7. Spread on the garlic butter and enjoy immediately while fresh and hot.