Clean and slice the leeks, using only the white and light green parts. Rinse thoroughly to remove any dirt.
Heat olive oil in a large skillet over medium heat. Add leeks and cook until soft and fragrant, about 6–8 minutes.
Add minced garlic and cook for 1 more minute, stirring frequently.
Stir in butter beans and pour in vegetable broth. Let simmer for 10 minutes, stirring gently.
Finish with lemon juice, thyme, salt, and pepper. Add sausage at this point if using.
Serve warm with crusty bread or a fresh salad.