In a large saucepan over medium heat, melt butter. Add garlic, thyme, cayenne pepper and smoked paprika; cook and stir until fragrant, about 1 minute.
Stir in chicken broth and half-and-half cream; bring to a boil. Reduce heat to low and simmer for 15 minutes.
Add green beans and simmer until tender, about 10 minutes more.
In a small bowl, whisk together flour and 2 tablespoons cold water until smooth. Slowly stir flour mixture into the soup; cook until thickened, about 10 minutes.