Heat oil in a deep 12-inch skillet over medium heat. Brown sausage links for 6 to 8 minutes, turning to color several sides, then transfer to a plate while partly cooked.
Add onion and both peppers to the same skillet and cook for 7 minutes, stirring occasionally, until their edges soften. Stir in garlic for 30 seconds.
Pour in wine and simmer for 2 minutes, scraping the bottom. Add broth, oregano and pepper and return sausage with its juices.
Cover and simmer over medium-low heat for 10 to 12 minutes until the center of each sausage reaches 160°F. Stir beans carefully into the spaces around the links.
Uncover and simmer for 3 to 5 minutes until beans are hot and the liquid lightly coats the vegetables. Stir in vinegar and serve one link with one-quarter of the peppers and beans per person.