Remove the duck from the refrigerator 30 minutes before cooking to bring it to room temperature. Preheat the oven to 350°F (175°C). Rinse the duck under cold water and pat completely dry with paper towels—dry skin is essential for crispiness.

Using a sharp knife, score the duck skin in a shallow crosshatch pattern, being careful not to cut into the meat. Prick the fatty areas several times to help render the fat. Season generously with salt inside and out. Stuff the cavity with smashed garlic cloves and lemon halves. Tie the legs together with kitchen twine.

Place the duck breast-side up on a roasting rack set in a roasting pan. Roast for 40 minutes. Flip the duck breast-side down and continue roasting for 20–40 minutes, until the thickest part of the thigh reaches 140°F (60°C).

While the duck roasts, whisk together the balsamic vinegar, lemon juice, and honey until smooth. Set aside.

Remove the duck from the oven and transfer it to a cutting board. Carefully pour off the rendered duck fat into a heatproof container (save for later use). Wipe the roasting pan clean.

Return the duck to the pan, breast-side up, and brush generously with the balsamic glaze. Roast for 20 minutes, brushing every 10 minutes. Continue roasting and brushing every 5 minutes for another 20 minutes, until the internal temperature reaches 155°F (68°C) and the glaze is caramelized and glossy. Broil for 5–10 minutes if extra crisp skin is desired (watch closely).

Remove the duck from the oven and rest for 15 minutes. Discard the garlic and lemon, carve, and serve immediately.