Preheat the oven to 450 degrees F with a large rimmed baking pan inside.
Put the olive oil, garlic and rosemary in a small saucepan and warm over medium heat until just starting to bubble. Turn off the heat and let steep 20 minutes. Discard the rosemary sprigs and garlic.
While the oil is steeping, cut the potatoes into 1-inch-thick wedges. Put the potatoes in a large bowl and toss with the oil, paprika and 1 teaspoon salt.
Carefully remove the baking pan from the oven and spread the potatoes on the hot pan in a single layer. Sprinkle with another pinch of salt and roast until the undersides are golden brown, about 20 minutes. Flip the potatoes and continue to cook until golden brown all over, 15 to 20 minutes more.