01 - Heat olive oil or butter in a large skillet over medium heat until shimmering.
02 - Add sliced leeks and diced carrot. Sauté for 5–7 minutes, stirring frequently, until leeks are soft and translucent but not browned.
03 - Stir in minced garlic and cook for 1 minute until fragrant, being careful not to burn.
04 - Add butter beans, thyme, salt, and black pepper. Stir gently to combine without breaking the beans.
05 - Pour in vegetable broth and bring to a gentle simmer. Cover and cook for 10 minutes, stirring occasionally, until heated through and flavors meld.
06 - Uncover the skillet, add lemon zest, and simmer for another 2–3 minutes to allow the sauce to thicken slightly.
07 - Taste and adjust seasoning as needed. Sprinkle with fresh parsley just before serving.