Peel 2 medium turnips, and cut into wedges. Halve the baby potatoes.
Preheat oven to 450° F.
Heat 2 tbsp olive oil in a small skillet over medium. Add garlic cloves and paprika; cook until fragrant, about 2 minutes. Set aside.
Combine turnips, potatoes, and garlic oil in a large bowl; toss. Place a baking sheet lined with parchment paper. Bake until golden, about 20 minutes, stirring halfway through. Check to see if they are cooked all the way through by piercing with a knife. Roast for an additional 5-10 minutes as needed until they are tender.
Toss with fresh parsley, lime juice, and sea salt and serve.