Braised leeks are incredibly simple and deceptively tasty. While perfect as a side dish, I like to turn them into a simple and nutritious whole food dinner by adding a poached egg.
Prepare the leeks. Trim the dark green leaves from the top and the root ends at the bottom. Peel off the tough outer layer, then slice in half lengthwise. Rinse the interior layers under cool running water to remove any sand, dirt, or grit, then pat dry.
Heat a 12” cast iron skillet over medium high heat. Add the butter and heat until it melts, foams, and the foam subsides. Add the leeks, cut side down, and saute until lightly browned, 3-4 mins. Flip the leeks and sprinkle with salt. Saute until the uncut sides are lightly browned, 3-4 mins.
Flip the leeks again, and add ½ c. dry white wine to the pan. Saute until the bubbling subsides, about a minute. Add the broth, increase the heat to high, and bring the liquid to a simmer (about a minute). Reduce the heat to medium low, or until the liquid is at a soft consistent simmer. Cover and braise until the leeks are very soft - they’ll be ready when they can be easily pierced with a knife tip, 20-25 mins.
While the leeks are cooking, poach the eggs. Fill a saucepan with about 6 cups of water and bring to a simmer over medium heat. Meanwhile, line a plate with a few paper towels. When the water comes to a rapid simmer, add 1 teaspoon white vinegar to the water. Crack an egg into a ramekin. With a spoon, stir the water to create a whirlpool, and then gently tip the egg, whites first, into the center of the whirlpool. Set a timer for 3 minutes and do not touch the egg. When the timer goes off, remove the poached egg with a slotted spoon and place on the paper towel lined plate. Bring the water bath to a simmer again, and repeat the poaching process with the remaining eggs, setting each finished egg aside on the paper towel.
Remove the leeks with tongs and transfer to a platter or divide between four plates. Add the thyme leaves, lemon zest, and lemon juice to the pan juices and increase the burner to medium high. Simmer until the sauce is slightly reduced and the thyme leaves have wilted.
Pour the pan sauce over the leeks, and top with fresh chives, cracked black pepper to taste, 1 tablespoon parmesan cheese, and a poached egg. Serve immediately.