Dissolve yeast and sugar in water in bowl of a stand mixer.
Add 2 cups flour, salt, olive oil, garlic powder, and basil.
Attach dough hook, and mix for approximately 1 minute on speed two.
Add more flour, as needed, until dough clings to hook and cleans side of bowl.
Knead for an additional 2 minutes on speed 2.
Place dough in a greased bowl, turning so that top of dough is greased.
Cover with plastic wrap, and place in a warm place to rise for 1 hour.
After hour, preheat oven to 400.
Place an inverted baking sheet in oven on middle rack.
Combine 1 cup mozzarella, cheddar, parmesan, garlic powder, and pinch of salt in a small bowl.
Coat a work surface with flour.
Place half of the dough on the prepared surface, and roll into a 12"x8" rectangle.
Transfer dough to a piece of parchment paper on a cutting board.
Sprinkle 1/2 cup of mozzarella on one half of the dough, so that 12"x4" is covered.
Fold uncovered half over cheese.
Sprinkle top with half of the cheese mixture.
Transfer parchment paper and dough to inverted baking sheet.
Bake for 15 minutes.
When dough is golden, remove from oven and place on cooling rack.
Repeat assembly with other half of dough and remaining cheeses.
Allow to cool for 1-2 minutes, then serve warm.