Place a large, empty roasting pan in the oven and preheat the oven to 450F.

Rinse the potatoes under cold water to remove excess starch and add them to a large stock pot. Cover the potatoes with cold water and add 2 tablespoons kosher salt and baking soda and set over high heat. Bring the water to a boil and cook the potatoes until they are just barely fork-tender and the edges start to flake, around 25 minutes total. Drain the potatoes and let them dry fully in the colander.

Remove the preheated roasting pan from the oven, add the duck fat and let it heat until melt. Gently shake the potatoes in the colander to rough up the edges then carefully add them to the roasting pan. Season the potatoes with a pinch of salt and pepper and gently toss them to coat. Nestle in the head of garlic, cut-side down, and return the roasting pan to the oven. Cook, tossing the potatoes every 20 minutes, until the potatoes are deeply golden brown and crispy all over, 55 to 60 minutes total.

Remove the garlic and push out the individual cloves. In a bowl, combine the roasted garlic cloves, chopped rosemary and olive oil. Use a fork to mash everything together then add the mixture to the roasting pan and toss with the potatoes to coat. Return the roasting pan to the oven and cook an additional 5 minutes or until the rosemary is fragrant and the garlic is lightly toasted.

Taste the potatoes for seasoning and adjust with flakey sea salt as desired. Transfer the potatoes to a serving bowl and enjoy.