Simple potatoes become a luxurious side when they’re roasted in duck fat till golden and pillowy soft. With silky ribbons of caramelized shallots, sweet cloves of roasted garlic, meaty oil-cured olives, and thyme, this dish will fill your kitchen with intoxicating aromas.
Preheat the oven to 350 degrees F. Use a paring knife to remove the peel from the garlic and shallots. Remove the root-ends of the shallots, then thinly slice. Add duck fat to a medium heavy-bottomed pot over high heat. Add the garlic cloves and cook, stirring often, until garlic begins to brown, 2–3 minutes. Reduce heat to medium; add sliced shallots and ½ tablespoon salt. Stir to combine with the duck fat and cook, 3-4 minutes. Then turn heat to low and cook until lightly caramelized, about 20 minutes.
After 20 minutes, the shallots should have light caramelization and the garlic cloves should be soft and golden brown. Remove from heat. Place potatoes in a baking dish large enough to hold them in an even layer. Pour the duck fat mixture over the potatoes, followed by wine and stock. Season with remaining ½ tablespoon salt. Lay thyme sprigs over the top, then tightly cover with aluminum foil. Roast for 1 hour.
After 1 hour, remove potatoes from the oven. Check for doneness by piercing a larger potato with a knife. If there’s no resistance, the potatoes are done. Discard thyme sprigs; then mix in the olives. Let rest so the flavors marry together, 1 hour. Rewarm in oven at 350 degrees F for about 10 minutes before serving.
This dish can be made 1 day ahead, cooled, and refrigerated overnight. Reheat in oven at 350 F until warmed through, 15–20 minutes.