My family is Polish.
My recs?
Zurek or bialy barszcz (white borscht) is one of my favorite soups. It’s a sour soup made by fermenting rye (like a very watery sourdough starter) and you can add meat (usually in the form of white unsmoked Polish sausage, or smoked Polish sausage/ribs to it), as well as potatoes and often hard-boiled eggs. Love this.
Barszcz (red borscht). This is different than other styles. It is a clear, red beet soup, almost like a consumme. It may have grated beets in it. It is also often served sour, as the beets are allowed to ferment for awhile in a jar, so they have a natural pickly sourness to them. On the same you will often get a croquette with minced beef in it. Or it can be served with tortellini-like pasta called uszka. They may be meat or mushroom filled (there are both vegetarian and beef-stock based versions of borscht available.) Kind of like a Polish tortellini al brodo.
Placek po wegiersku (Pancake Hunagrian style). I’ve lived in Hungary for over five years, and never actually seen this there, but the Polish dish is a potato pancake served with a stew version of Hungarian goulash (what the Hungarians would call pörkölt) over it. Great comfort food.
Golabki: Stuffed cabbage rolls. They are most typically stuffed with ground beef and/or pork with rice, but lots of variations exist. My mother makes a barley and wild mushroom version for vegetarian holy days (Christmas Eve.) They are served with either a sour cream sauce, a mushroom sauce, a tomato sauce, their own juices, or some combination thereof.
Pierogi: I assume most people know what this is. Basically Polish ravioli. My favorite are Ruskie Pierogi (“Ruthenian pierogi”) which are stuffed with potatoes and fresh cheese (like a ricotta or cottage cheese type thing.) They can additionally be fried in bacon, but I just like them plain and boiled, served with sour cream on the side.
Now, Hungary is not my nationality, but I’ve spent a number of years there (as I noted above.) For that I would say:
Gulyasleves: The soupy form of goulash.
Langos: A savory elephant ear. It’s deep fried potato dough served with at least garlic water and salt, but often also sour cream, cheese, and other toppings like ham.
Paprikas csirke: Chicken Papriksh. A simple meal of stewed/braised chicken in a sour cream, onion, and paprika sauce, usually served with noodles called galuska or nokedli on the side (spaetzle, for the people who know German food.)
Töltött karalabé: Stuffed kohlrabi. It’s kohlrabi hollowed out, stuffed with a meat and rice mixture, served in a sour cream sauce. Perhaps my favorite Hungarian comfort food.