Heat olive oil in a large pot or deep skillet over medium heat.
Add the sliced smoked sausage and cook for 5 minutes, stirring occasionally, until browned.
Add the diced onion and minced garlic to the pot and cook for 2-3 minutes until the onion is softened.
Add the halved baby potatoes to the pot and stir to combine with the sausage and onions.
Sprinkle smoked paprika, dried thyme, salt, and black pepper over the mixture and stir well.
Pour in the chicken broth, cover the pot with a lid, and let it simmer for 15 minutes, stirring occasionally.
Add the trimmed green beans to the pot, stir to combine, then cover and cook for an additional 10 minutes, or until the potatoes are tender and the green beans are crisp-tender.
Remove the lid and cook for 2-3 minutes more to allow any excess liquid to evaporate.
Taste and adjust seasoning if necessary before serving.