Preheat the oven to 375 degrees F. Grease two spots in a muffin tin.
Prepare the dough: mix together the flour and cinnamon in a medium mixing bowl, then add the Greek yogurt. Stir together until a shaggy dough forms, then knead by hand for a few minutes until the dough forms a ball that is not sticky and workable.
Pour dough out on a floured work surface, and sprinkle a little more flour on top. Roll the dough into a large rectangle, about 5 inches wide by 12 inches long, cutting the edges of the dough if needed to form the rectangle.
Cut the rectangle in half lengthwise so you have two strips, each about 2 ½ inches by 12 inches.
Let the dough sit for now while you get the ingredients ready for the filling. In a small bowl, combine the melted butter, brown sugar, and cinnamon. Spread the cinnamon sugar filling over both strips of the dough.
Slice the apples lengthwise into thin pieces (skipping over the core). Cut each slice in half again widthwise. Place the apple slices on a microwave safe plate, cover with a damp paper towel, and microwave on high for 45 seconds to make the slices pliable and easy to work with.
Place the apples along the long edge of the strip of dough so that the rounded edge of the apple is slightly overlapping the edge of the dough, and so that each apple slice overlaps the one before.
Start from the top and carefully roll the dough down to the end. Place this in the greased muffin tin and repeat with the other strip of dough.
Bake the apple roses at 375 degrees F for 16 to 18 minutes, or until the dough is fully cooked through and turning golden brown on the edges. Let cool in the pan for 5 minutes, then carefully remove and serve.