Prepare the marinade by combining the garlic, vinegar, and rosemary in a bowl. Using a sharp knife, score the skin of the duck breasts in a crisscross pattern. Place the duck breasts skin-side down in a shallow dish and spoon the marinade over them. Cover and refrigerate for 30 minutes.

Transfer the duck breasts to a frying pan, placing them skin-side down along with any remaining marinade. Cook over medium-high heat for 5–7 minutes until the skin is crispy and golden. Flip the breasts over and cook for an additional 5 minutes on the other side. Remove the duck from the pan and set aside in a warm place to rest.

Carefully spoon off any excess fat from the frying pan, leaving just the flavorful cooking juices behind. Pour in the stock and wine, then increase the heat to high and boil rapidly until the liquid reduces to a dark, syrupy glaze. Stir in the tomato paste and lemon juice to add depth and brightness to the sauce.

Take the pan off the heat and whisk in the butter, a little at a time, allowing it to melt slowly into the sauce and create a rich, velvety texture. Taste and adjust the seasoning with salt and pepper as needed.

Slice the rested duck breasts diagonally into thin pieces and arrange them attractively on warmed serving plates. Spoon the glossy sauce around the sliced duck, sprinkle with freshly chopped rosemary for garnish, and serve alongside boiled potatoes and green beans.