Melt butter in a large pot over medium heat. Once melted, add the onion, celery, carrots, salt, Italian seasoning and pepper. Stir well and sauté for 6-7 minutes, until the vegetables start to soften.
Add in vegetable broth and lemon juice. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes.
While the soup is simmering, make the dumplings. In a medium bowl, stir together flour, baking powder and salt. Add the butter to the flour mixture, using your hands to cut the butter into the flour until no big lumps remain. (Don't overwork the dough – the butter doesn't have to be completely incorporated.)
Stir the spinach, peas and parsley into the soup.
Form dumplings into small rounds (about 2 teaspoon of dough per dumpling), then drop into the soup. Bring soup to a boil again, then reduce to medium low and cover.