Trim off the dark green tops and stringy roots, leaving the base intact to prevent the leeks from falling apart. Halve them lengthwise, then soak in cold water to remove grit. Let dry completely.

Sprinkle the cut side of the leeks with sugar, salt, and pepper. Heat 3 tablespoons of olive oil in a large pan over medium heat. Add the leeks cut-side down in a single layer, along with the lemon slices. Cook for 5-6 minutes until golden and caramelized, flipping the lemon halfway.

Pour in the wine, vegetable broth, and thyme. Season lightly with salt and pepper, then cover the pan and reduce the heat to low. Simmer for 15 minutes, flipping the leeks halfway through. Check for doneness with a knife—it should glide through easily.

Remove the leeks and lemon slices, keeping them warm under foil. Simmer the remaining liquid until it thickens slightly, then stir in the remaining olive oil, lemon juice, and chives.

Arrange the leeks on a platter, drizzle with the sauce, and sprinkle with feta and dill (if using). Serve warm, and enjoy!