Heat oil in large saucepot over medium-high heat; add sausage and cook 4-6 minutes, turning occasionally, or until brown on all sides. Transfer sausage to plate.
Return saucepot to heat; add onion, mushrooms and carrots, and cook 8 minutes, stirring often, or until tender. Add broth, thyme, bay leaf, beans, tomatoes and sausage; cover and bring to a boil. Reduce heat to low and simmer, stirring occasionally, 8-10 minutes or until carrots are tender.