I don't know the size of your New Zealand meat pie, it doesn't look hand held, but looks delish, I would try it. Im Polish and was introduced to the Pierogi as a kid, my favorite being the potato and cheese. Although these Polish traditional dumplings did not come with meat filling, they do now apparently, but wouldn't that be more like Ravioli, a traditional Italian pasta. A dumpling (dough) is much heartier than pasta, I have yet to try a ground meat filled one, they are kind of bland and do require seasoning if preferred
These became so popular, that now I see Pierogi in the frozen section of super markets. My Polish granny made them for years
Pierogi (pronounced /pɪˈroʊgi/ pi-ROH-ghee, in Slovakia pi-ROH-hee), also known as varenyky, are filled dumplings of East European origin. They are made by wrapping pockets of unleavened dough around a savory or sweet filling and cooking them in boiling water. These dumplings are popular in Slavic (Polish, Slovak, Ukrainian, Russian), Baltic (Latvian, Lithuanian) and other Eastern European cuisines (such as Romanian) where they are known under local names. Pierogi are especially associated with Poland, Ukraine, Slovakia and Canada where they are considered national dishes.
Pierogi are often semi-circular but triangular and rectangular ones are also found. Typical fillings include potato, sauerkraut, ground meat, cheese and fruits. The dumplings may be served with toppings, such as melted butter, sour cream or fried onion. The traditional savory method is with onion, and sweet method with sour cream.
Pierogi may be stuffed (singularly or in combinations) with mashed potatoes, fried onions, quark (sometimes called farmers cheese), cabbage, sauerkraut, meat, mushrooms, spinach, cheese, or other ingredients depending on the cook's preferences. Dessert versions of the dumpling can be stuffed with sweetened quark or with a fresh fruit filling, such as cherry, strawberry, saskatoon berry, raspberry, blueberry, peach, plum, or apple; stoned prunes are sometimes used as well as jam. For more flavor, sour cream can be added to the dough mixture, and this tends to lighten the dough