In a large skillet, heat oil over medium-high. Add sausage and cook until browned on all sides, about 8 minutes. Transfer to a plate. Add carrots and shallots to skillet and cook until beginning to soften, about 4 minutes:season with salt and pepper. Add garlic and cook until fragrant, about 1 minute. Add black beans and broth and bring mixture to a boil. Add sausage, reduce heat to a rapid simmer, and cook until carrots are tender, about 12 minutes. Remove from heat and stir in parsley. Serve with more parsley and a dollop of yogurt.