Preheat oven to 300°F.
Combine parsnips, carrots, garlic, 2 rosemary sprigs, and 1 tbsp. salt in a baking dish; turn garlic cut side down.
Pour oil over. Roast 45 minutes.
Remove from oven and turn parsnips and carrots over, and take out the garlic and set aside to cool.
Return the parsnips and carrots to the oven and roast until a knife easily slides through flesh, another 45 minutes.
Meanwhile, bring currants, sugar, ½ cup vinegar, remaining 1 tsp. salt, remaining rosemary sprig, and ¼ cup water to a boil in a small saucepan over medium-high heat.
Reduce heat and simmer until reduced by three-quarters.
Transfer to a small bowl and stir in remaining 1 tbsp. vinegar.
After 45 minutes, remove parsnips and carrots from the oven, and after letting them cool for a short while, remove them from the baking dish, letting excess oil drip off, and place on a rimmed baking sheet.
Heat a large skillet, preferably cast iron, over medium-high.
Arrange a few parsnips and carrots in skillet in a single layer and cook, turning occasionally, until golden brown and charred in spots, for about 4 minutes, repeating this step in batches until all the parsnips and carrots are golden brown. (Alternatively, you can broil them, turning halfway through, 10–12 minutes.)
Transfer to a platter and spoon the currant sauce over.
Top with reserved garlic and rosemary leaves.