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 2 minutes of kneading). If dough is too sticky to knead, add more flour, 1 Tbsp 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 4 equal pieces. Use a rolling pin to roll each piece of dough into a 6-7 inch 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 ¼ c sauce, 3 Tbsp mozzarella cheese and 5 pieces pepperoni. Return to oven and bake a few more minutes until dough is cooked through and cheese is melted.
Serve each sprinkled with 1 Tbsp Parmesan, 1/2 Tbsp basil and a pinch red pepper flakes.