Make the pasta dough: Combine the eggs, flour, water, olive oil, and 1 1⁄2 teaspoons of salt in a stand mixer fitted with the hook attachment. Mix on the lowest speed for 6 minutes, until all the flour is hydrated and a dough begins to come together. Increase to second speed and continue mixing until dough is smooth and quite elastic, about 5 minutes more. Wrap the dough loosely in plastic and rest 1 hour before rolling it out.
Meanwhile, make the filling: In a medium bowl, combine the lamb with the grated onion, salt, Baharat, and black pepper. Mix well with your hands or a wooden spoon and refrigerate until you are ready to shape the dumplings.
Make the dumplings: Line two sheet pans or cookie sheets with lightly oiled parchment paper and preheat oven to 425°. Divide the pasta dough into three equal pieces; keep the remaining dough covered as you work. On a very lightly floured surface, use a rolling pin to roll 1 piece into a thin, even rectangle measuring 11 1⁄2-by-16 1⁄2 inches. Trim the edges and cut the rectangle into 15 3-by-3-inch squares. Place about 2 teaspoons of lamb filling in the center of one square, then fold the four corners up to meet in a point, pressing the edges tightly together to make a neat parcel. Continue shaping the remaining squares, then repeat with the remaining dough. Space the dumplings evenly on the prepared pans and bake in the preheated oven for 12–14 minutes, until they are lightly toasted.
Bring a large pot of salted water up to a rolling boil. Cook the dumplings in batches of 15; boil for 6–8 minutes, till the pasta is tender. Scoop the cooked dumplings out of the pot using a slotted spoon and set back on the lined sheet trays as you continue cooking the remaining dumplings. When they have all been boiled, stir 1⁄3 cup of the cooking water into the seasoned yogurt to thin and warm it a bit. If the tomato sauce has cooled, gently rewarm it over a low flame.
To serve, divide the yogurt sauce evenly between 6 bowls. Add 7–8 manti to each dish, followed by 1⁄4 cup of tomato sauce. Sprinkle the pasta generously with mara pepper, dried spearmint, and sumac, and serve immediately.