Make the sauce: In a small (1- or 2-quart) saucepan, heat the 1-1/2 tablespoons olive oil over medium heat. Add the onion, carrot, and garlic and cook, stirring frequently, until softened but not browned, about 5 minutes. Add the wine and let it reduce until almost evaporated, about 1 minute. Add the pimentón and cumin and stir for about 15 seconds. Add the tomatoes and juice, thyme sprigs, sugar, Tabasco, 1/4 teaspoon kosher salt, and a few grinds of pepper.
Reduce the heat to a gentle simmer and cook, uncovered, stirring occasionally, to reduce the sauce somewhat and intensify its flavor. This should take about 1 hour; depending on how much juice you started with, you may need to add up to 12 cup water during simmering to keep the consistency saucy rather than dry.
Fish out the spent thyme sprigs. Purée the sauce with an immersion blender or a regular blender until it’s smooth and creamy; you can thin with a little water if needed. Stir in the sherry vinegar. Taste and add salt and pepper, if needed. The sauce should be slightly spicy, and you should have about 1-1/2 cups.
Roast the potatoes: Heat the oven to 425°F. Toss the potatoes with the olive oil, 1 teaspoon kosher salt, and the rosemary (if using) on a large rimmed baking sheet. Roast, turning the potatoes with a metal spatula every 15 minutes, until they’re browned and crisp outside and tender inside, about 45 minutes.
Put the potatoes in a serving dish and put the sauce in a small dish next to the potatoes, along with a spoon.