This isn't barley, it's pasta. You could also use orzatta. You can also dry the dough and grate it with a box grater. Barley and kasha used to be the staples of Eastern Europe; potatoes and pasta replaced them.
Roll out pasta dough 1/4-inch thick. With a pizza wheel and ruler, cut into 1/4-inch strips. Let the pasta dry a little, and then cut it into 1/4-inch squares with a knife. Boil until tender. Drain.
In a saute pan, heat the olive oil. Brown the onions, then add the garlic, carrots, parsnip, and mushrooms. Cook until barely tender. Add the pasta and heat through.
Put the flour in a mixing bowl, and make a well in the center. Mix in the rest of the ingredients to form a soft dough. Knead until elastic. Form into a disk and wrap with plastic. Refrigerate for 1 hour to relax.