Sauté the sausage in a large pot over medium heat until browned all over, about 5-7 minutes.
Add chopped onions, carrots, celery, and minced garlic; stir occasionally until softened and fragrant, about 5 minutes.
Add diced tomatoes with their juice and pour in vegetable broth; bring to a gentle boil while stirring occasionally.
Stir in Italian seasoning along with salt and pepper to taste; let it simmer for about 10 minutes.
Add spinach or kale right before serving; let it wilt into the warm broth for about two minutes.
Ladle generous portions into bowls and enjoy.