Preheat the oven to 400°F.Put the potatoes in a large microwaveable bowl with ½ cup water and cover with parchment paper. Microwave for 5 minutes. Drain the potatoes and rinse them with cold water until they no longer feel warm to the touch and pat them dry.While the potatoes are in the microwave, put the duck fat on a large, rimmed baking sheet and place it in the oven for about five minutes to warm up.Carefully add the potatoes to the hot baking sheet and mix with a spatula to coat them with the duck fat. Roast for 30 minutes, then flip the potatoes and raise the oven temperature to 450°F. Roast for 15-25 more minutes, or until the potatoes are a rich golden brown on the outside but tender and fluffy on the inside. Drain the potatoes on paper towels and sprinkle them liberally with sea salt.While the potatoes are roasting, prepare the sauces. To make the salsa brava, heat the olive oil in a small saucepan over medium heat. Add the remaining ingredients and cook, stirring frequently, for 3-5 minutes. Taste and adjust seasonings as desired.To make the allioli, whisk all the ingredients together in a bowl.Serve the potatoes hot topped with dollops of both sauces and a sprinkling of fresh herbs.