Preheat the Oven:
Place a large empty roasting pan in the oven and preheat to 450°F (230°C).
Parboil the Potatoes:
Rinse the potatoes under cold water to remove excess starch. Transfer them to a large stockpot and cover with cold water. Add the kosher salt and baking soda. Bring to a boil over high heat and cook for about 25 minutes, or until the potatoes are barely fork-tender and the edges begin to break down slightly.
Drain and Dry:
Drain the potatoes thoroughly and allow them to sit in the colander for a few minutes to dry completely.
Roast the Potatoes:
Carefully remove the hot roasting pan from the oven. Add the duck fat and allow it to melt. Shake the potatoes gently in the colander to rough up the edges, then transfer them to the roasting pan. Season with a pinch of salt and black pepper and toss gently to coat. Place the garlic head cut-side down among the potatoes.
Cook Until Crispy:
Return the pan to the oven and roast for 55–60 minutes, tossing the potatoes every 20 minutes, until deeply golden brown and crispy on all sides.
Prepare the Garlic-Rosemary Mixture:
Remove the roasted garlic from the pan. Squeeze the softened cloves into a small bowl and combine with the chopped rosemary and olive oil. Mash with a fork until a paste forms.
Finish Roasting:
Toss the garlic-rosemary mixture with the potatoes. Return the pan to the oven for 5 more minutes, allowing the rosemary to become fragrant and the garlic to lightly toast.
Serve:
Taste and adjust seasoning with flaky sea salt as desired. Transfer to a serving dish and serve immediately.