Preheat the oven to 425°F (220°C) and line a sheet pan with a silicone mat or parchment paper.
In a medium mixing bowl, whisk together the flour, baking powder, and kosher salt until evenly combined.
Add the Greek yogurt to the dry ingredients and mix with a fork or spatula until a crumbly dough forms.
Turn the dough onto a lightly floured work surface and knead a few times (about 20 turns) until smooth and tacky but not sticky.
Divide the dough into 4 equal portions (about 3–3/8 ounces each) and shape each into a ball.
On a lightly floured surface, roll each ball into a 7-inch diameter thin round with a rolling pin.
Spoon about 1 tablespoon marinara sauce in a strip down the center of each round. Top each with 2 ounces (about 1/2 cup total across rolls) sliced grilled chicken, an additional 1 tablespoon marinara, and 3 tablespoons shredded mozzarella.
Fold the right side of the dough over the filling, then fold the left side over to enclose the filling and form a roll.
Beat the large egg and brush it over the tops of the rolls, then sprinkle with sesame seeds.
Bake on the prepared sheet pan until golden, about 20 minutes. Serve hot.
