Beat together the eggs, water, salt, and olive oil.
To make the dough by hand, fill a large mixing bowl with the flour and make a well in the center. Add the wet ingredients to the well. Slowly incorporate the flour into the wet ingredients until a ball of dough is formed. Alternatively to make the dough in a stand mixer fitted with the dough hook attachment, add the flour to the mixer bowl, then add the wet ingredients and mix for 3 to 4 minutes until smooth and pliable. If the dough is sticky add a bit of flour as needed, and continue to mix/knead the dough until smooth. Cover the dough with a tea towel and set aside for 30 minutes.
Mix together the ground beef, onion, parsley, salt, pepper, and paprika until well incorporated. Refrigerate until needed.
Preheat the oven to 400°F and place the oven rack in the center of the oven. Grease 2 (13 by 9-inch) baking pans or 1 larger (13 by 18-inch) pan with butter and set aside.
Using a hand-cranked pasta roller or a rolling pin, in batches roll out the dough until it's very thin, dusting the dough with flour as needed. If using the Kitchenaid pasta roller attachment, roll until #4 for thickness (see notes below).
On a lightly floured surface, cut each strip of dough into 1 ½ inch squares. Place a ½ teaspoon of meat filling into the center of each square and pinch the two ends with your fingers to form a canoe-shaped dumpling.
Repeat with the remaining dough and meat filling. Arrange the manti close together in the buttered pans. Dot the tops of the manti with bits of butter, and bake for about 40 to 50 minutes, or until golden brown.
Meanwhile, mix the yogurt and garlic, and season with salt. Set aside.
Add the chicken broth and water to a saucepan and season with salt and pepper. Bring to a simmer.
When the manti are golden brown, remove the pans from the oven and ladle the broth mixture over the manti. The broth should fill the pan about ¾ of the way up the manti. Reserve the rest of the broth for serving.
Return the pans to the oven and bake for 10 minutes longer until most of the broth is absorbed into the manti, and about ¼-inch of broth (or less) remains on the bottom and the manti have slightly plumped up. They will have a firmer than al dente texture, with a slight crunch at the ends, but you can bake them longer with the broth if you want a slightly softer texture.
Remove the pans from the oven and serve manti in individual wide bowls, ladling some more of the hot broth over it. Top with yogurt-garlic sauce and sumac. Enjoy!