Heat olive oil in a large pot over medium heat.
Add diced onion and sauté until translucent, about 5 minutes.
Stir in minced garlic and cook for another minute.
Add ground beef or turkey, breaking it up, and cook until browned.
Incorporate diced tomatoes, broth, carrots, and celery.
Bring the mixture to a boil, then reduce the heat to a simmer.
Add the chopped cabbage and thyme, stirring to combine.
Season with salt and pepper to taste.
Cover and let simmer for about 30 minutes, stirring occasionally.
Serve hot, garnished with fresh herbs if desired.