Vegetable Soup

Without a significant amount of meat [or no meat at all]

Brocho before eating this: Borei Pri Ha'adama

Brocho after eating the proper shiur of this: Borei Nefashos

With significant amount of meat when eaten together with soup

Brocho before eating this: Shehakol Niyeh Bedvoro

Brocho after eating the proper shiur of this: Borei Nefashos

With meat, if vegetables and meat are eaten separately

Brocho before eating the vegetables: Borei Pri Ha'adama

Brocho before eating the meat: Shehakol Niyeh Bedvoro

Brocho after eating the proper shiur of this: Borei Nefashos

Source: The Laws of B'rachos (page 381)