In a bowl place the flour, egg, salt and water. Knead about 10 minutes till you get a firm and smooth dough. Cover it with a moist towel and rest it 20 minutes.
While the dough is resting, mix all the filling ingredients in a plate and set aside to use at makingTepsi Mantı dumplings.
Pre-heat the oven to 200 C (or 400 F).
Divide the dough into 4 pieces. Take one dough and place on the floured counter. Don't forget to cover rest of the dough. Then flatten the dough with a flat surface rolling pin as thin as you can.
Cut the flatten dough with knife into 3/4 inch (about 2 cm) square pieces. Then use 1/4 of a teaspoon to fill each squares. Then stick the upper and lower corners of the each square by pressing with your finger tips. Do the same steps for remaining dough pieces. They will look like a boat/canoe shape.
Grease (12-inch) baking pan with butter and set aside.
Arrange the manti dumplings close together in the buttered pan. Dot the tops of the manti dumplings with bits of butter, and bake for about 30 minutes, or until golden brown.
While manti dumplings are cooking in the oven, you can able to prepare both yogurt and tomato sauce.
In a bowl; pour the yogurt and garlic. Mix them well.
In a skillet; put the butter first and then add the paprika powder, tomato paste, salt and water. Cook them about 5 minutes at medium heat.
When the manti dumplings are golden brown color, remove the pan from the oven and ladle tomato sauce mixture over the manti dumplings evenly. The tomato sauce will fill the pan for about 3/4 of the way up the manti dumplings. Return the pan to the oven and bake for 10 minutes longer until most of the tomato sauce is absorbed into the manti dumplings, and about 1/4-inch of tomato sauce remains on the bottom.
Remove the pan from the oven and pour yogurt topping. (If you want, you can serve yogurt individually for each serving plates)
If it is requested, sprinkle some dried mint and sumac over the Tepsi Mantı.