Heat a few T olive oil in a large dutch oven over medium heat. When oil is shimmering, add sausage, onion, green bell pepper, celery, and garlic. Cook for 4-6 minutes, until softened.
Stir in thyme, paprika, cayenne, bay leaves, salt and pepper, and cook an additional 30-45 seconds. Pour in chicken broth and give it a big stir.
In a separate small bowl, make your slurry by whisking the flour and water together until a creamy paste forms. Add to pot.
Bring to a boil, then reduce heat, cover and simmer for 20-25 minutes, until gumbo has thickened.
In the last 10 minutes of cooking, add shrimp. Once shrimp is pink and cooked through, adjust salt and pepper. Stir in green onions and vinegar.