In a food processor, add the flour, and salt and pulse to combine. Slowly add the butter 1 tablespoon at a time, pulsing between each addition of butter. In a small bowl whisk the egg, then add the egg to the flour and pulse until just combined. Slowly add the ice water 1 teaspoon at a time until the dough forms. Be careful to not overwork the dough.

Bring the dough to a lightly floured surface and roll into a ball, wrap in plastic and flatten. Allow it to chill in the refrigerator for about 30 minutes.

Preheat the oven to 400 degrees.

Slice the tomatoes about ¼ inch thick. Wash and dry the basil leaves - you can leave them whole or gently rip them in smaller pieces with your hands - do not use your knife to cut them! Break up the feta into small and medium-sized crumbles. Add salt and pepper to taste. Set everything aside.

Take out the dough and flatten until slightly over ¼ inch thick. Don't worry too much about the exact shape or edges - it is not supposed to be perfect. It should be around 12 inches in diameter.

Layer the tomatoes, basil and feta in the middle the the dough, leaving a 1 ½ inch border. Fold over the border over the tomatoes. Brush with extra virgin olive oil mixed with the minced garlic and oregano.

Bake for about 25 - 30 minutes, or until the crust is golden.