Rinse duck breasts and pat dry with paper towels. Place on a cutting board, skin side up. Use a sharp knife, score the skin with even strokes. Don’t cut through the meat.
Heat a cast iron skillet over high heat and pre-sear the skin side for 2-3 minutes. No need to add any oil. The duck breasts will produce enough fat.
Add thyme and garlic into the skillet, flip the breasts, sear the meat side for another minute. Let the fresh thyme and garlic toast in the duck fat at the same time.
Once the duck is pre-seared, turn off the heat and transfer the duck breasts to the cutting board. Season generously with salt and ground black pepper.
Place the prepared duck breasts into a sous vide bag, toss the thyme and garlic into the bag. Vacuum seal it using a vacuum sealer or a hand pump and lower the bag into the water bath. Set timer for 1.5 hours.
In the meantime, make mashed potatoes. Bring a pot of salted water to a boil. Add potatoes and cook until tender, about 15-20 minutes; drain.
In a small saucepan, heat butter and milk over low heat until butter is melted. Slowly add milk mixture into potatoes and mash until smooth and creamy. Season with garlic powder, salt, and pepper to taste. Set aside.
In the same skillet that you used to sear the duck breasts, melt 2 tablespoons butter over medium-high heat. Sprinkle the sugar and 1/4 teaspoon salt evenly over the bottom of the skillet.
When sous vide cooking is done, remove the cooked duck breasts from the bag and reserve the duck juice.
Sear the skin side in the same skillet over high heat until the duck skin is golden brown. Transfer to a clean cutting board.
Still using the same skillet (no need to wash), gently place leeks into the skillet in a single layer, cut side down. Cook over medium heat 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, reserved duck juice, and fresh thyme. Reduce the heat to low, cover and simmer until the leeks are tender and translucent, about 10 minutes.
Gently transfer the leeks to two serving plates evenly, 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 and lemon juice in the skillet. Once the butter is melted, stir and season with salt and pepper to taste.
To serve, slice the duck breasts along the scores in the skin and place on the serving plates with the leeks. Scoop some mashed potatoes to put on the side. Pour the leek cooking liquid over and enjoy!