Preheat oven to 375ºF. Line a baking sheet with parchment paper.
Place yogurt and flour in a large bowl; stir well with a wooden spoon until just combined and then keep mixing dough in bowl with your hands until smooth (about two minutes of kneading). If dough is too sticky to knead, add more flour, one tablespoon at a time, until no longer sticky.
Place a large piece of parchment paper on a work surface and sprinkle with a little flour; place dough on paper. Use a knife to cut dough into four equal pieces. Use a rolling pin to roll each piece of dough into a 15-18 centimeter oval. Place on prepared baking sheet; bake until dough is beginning to turn lightly golden, about 18 minutes.
Remove from oven and top each with 1/4 cup sauce, three tablespoons mozzarella cheese and five pieces pepperoni. Return to oven and bake a few more minutes until dough is cooked through and cheese is melted.
Serve each sprinkled with one tablespoon Parmesan, 1/2 tablespoon basil and a pinch red pepper flakes.