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