i have been living in asuncion for a little over a year, and am going to share some local dishes:

they use yucca a lot (called manioc, actually mandioca, here)...

chipa guazu, which is a corn and cheese based bread (think cornbread, less sweet, with cheese)

sopa paraguaya (actually not a soup at all), similar to chipa guazu, yet more corn, no cheese, whole kernels

fried chopped meat with manioc in a patty

empanada, oh so many varieties... i personally like the oven baked spinach empanada

pascualina, which is like a giant empanada stuffed with about 7 green veggies and some cheese. i make mine whole wheat.

mbeju, a pancake like patty with a dry cheese (it is melted yet makes your mouth feel dry afterwards, weird) and corn meal i believe.

milanesa, which is a fried breaded chicken or beef cutlet.

the beef in famous in this part of the world, and the bife de chorizo is damn good.

overall, the traditional food is fried and highly beef driven. there are heaps of delicious local fruits and veggies; my faves are the mangoes, watermelon, and papaya