For the dough: Combine the flour, 1 cup water and a pinch of salt in a large bowl and mix with your hand until it comes together. Knead until the dough is smooth and no longer sticky, 1 to 2 minutes.
Flour a work surface and transfer the dough to it. Knead a few times and shape into a ball. Let rest for 10 minutes.
For the filling: Heat the vegetable oil in a large, heavy skillet. Add the onion and cook until translucent, stirring occasionally. Add the ground beef and season with salt, pepper and cinnamon and cook, stirring to break up any lumps, until browned and cooked through. Remove from the heat and let cool.
On a floured surface, roll out the dough to a thickness of about 1/8 inch (3.125 mm). Cut the dough into circles with a 5-inch round cutter to make about 30 dough rounds. If there is any leftover dough, reroll and cut more circles.
Fill a dough round with a spoonful of the meat mixture then fold the edges together to create a half-moon shape and seal well (do not overstuff the dough rounds). Repeat with the remaining dough rounds and filling.
For the sauce: Combine the yogurt, crushed garlic and sea salt to taste in a medium bowl. Spoon the yogurt mixture onto a serving platter and set aside.
Bring a large pot of water to a boil. Cook the shish barak in batches in boiling water for 2 to 3 minutes, until they are floating and tender.
While the dumplings simmer, heat 1 tablespoon butter and 2 tablespoons olive oil in a large nonstick skillet. Lift the dumplings from the water with a slotted spoon or skimmer, thoroughly strain and add to the heated pan (use caution, it could splatter). Fry the shish barak until crispy and golden, 2 to 3 minutes, flipping halfway. Transfer to the platter with the sauce. Repeat with the remaining shish barak.
Heat 2 tablespoons butter and 2 tablespoons olive oil in a small skillet over medium heat. Add the paprika and the pine nuts and cook, stirring constantly, until golden, 1 to 2 minutes. Pour the pine nut mixture over the shish barak.
Garnish with parsley leaves and a sprinkle of paprika. Serve immediately.