01 - Slice the leeks in half lengthwise and rinse thoroughly under running water to remove any grit.
02 - In a large skillet or sauté pan, melt the butter over medium heat, then add minced garlic and cook for 1 minute until fragrant without browning.
03 - Place the leeks cut-side down in the pan. Season evenly with salt, black pepper, and thyme.
04 - Pour in the vegetable broth and white wine if using, then bring to a simmer.
05 - Cover the pan, reduce heat to low, and braise for 25 to 30 minutes until the leeks are tender and most liquid is reduced.
06 - Uncover the pan and increase heat to medium-high for 2 to 3 minutes to slightly thicken the sauce if desired.
07 - Transfer the leeks to a serving dish, spoon the pan juices over them, and garnish with parsley and lemon zest if preferred.