In a large stock pot or dutch oven, add olive oil and heat on medium until light and shimmery.
Add onion and cook until soft, about 5 minutes.
Add garlic, celery, and carrots, and continue cooking for another 5-10 minutes, stirring occasionally, until fragrant, soft, and lightly browned.
Stir in sliced andoille sausage, mushrooms, and zucchini, and heat until they are lightly browned as well.
Season vegetables and meat with cumin, salt, dried oregano, and pepper.
Slowly pour in beef broth, scraping up any browned bits from the bottom of the pan.
Stir well and bring to a rolling boil, let reduce for about 5 minutes.
When soup has thickened slightly, remove from heat and ladle into bowls.
Serve immediately, enjoy!