Score the Duck Breasts: Use a sharp knife to carefully score the skin of each duck breast in a crosshatch pattern, spacing the cuts about ½ inch apart. Be cautious not to cut through the fat into the flesh.
Season and Marinate: Rub the duck breasts evenly with kosher salt and Chinese five-spice powder. Let them sit at room temperature for 30 minutes, or for a more developed flavor, cover and refrigerate overnight.
Prepare the Potatoes: In a large pot, bring salted water to a boil. Add the potato wedges and boil for 15–20 minutes until tender. Drain the potatoes well and arrange them on a baking sheet lined with a clean cloth to dry off any remaining moisture.
Preheat the Oven: Set your oven temperature to 350°F.
Render the Duck Fat: Heat a large skillet over medium heat. When the skillet is hot, place the duck breasts skin-side down into the pan and add the bay leaf. Allow the fat to render out and the skin to turn golden and crispy, which takes about 6 minutes. Flip the duck breasts and add the smashed garlic and a pinch of red chile flakes to the skillet. Transfer the skillet to the preheated oven and roast the duck for 3–5 minutes, or until the internal temperature reaches 125°F on an instant-read thermometer.
Rest the Duck: Remove the duck from the skillet and let it rest on a cutting board to allow the juices to redistribute.
Fry the Potatoes: Keep the skillet over medium-high heat, leaving the rendered duck fat and bay leaf in the pan. Lightly press the potato wedges with a fork or spatula to flatten them slightly, but avoid breaking them apart. Fry the potatoes in batches in the hot duck fat, cooking for about 3–4 minutes per side, until they are golden and crispy. Sprinkle with salt and freshly ground black pepper.
Assemble and Serve: Slice the duck breasts thinly and arrange them on a plate alongside the crisp potato cakes. Drizzle any juices from the skillet over the duck and potatoes before serving.