In a large skillet (ideally nonstick one), melt 2 tablespoons butter over medium-high heat. Sprinkle the sugar and 1/4 teaspoon salt evenly over the bottom of the skillet.
Gently place leeks into the skillet in a single layer, cut side down. Cook for about 5 minutes, shaking the skillet occasionally until the cut side of the leeks is golden brown. If your leeks brown too quickly, adjust the heat.
Now, add wine, chicken bone broth, fresh thyme, and bay leaf. Reduce the heat to low, cover and simmer until the leeks are tender and translucent, about 10 minutes.
Gently transfer the leeks to a serving plate, leaving the liquid in the skillet. Cover the leeks with foil and set aside.
Return the liquid to a simmer over medium-high heat. Add 1 tablespoon butter, parsley and lemon juice in the skillet. Once the butter is melted, stir and season with salt and pepper to taste. Spoon the sauce over the leeks and serve. Enjoy!
For a vegan version, substitute the butter for coconut oil and substitute the chicken broth for vegetable broth.