Preheat the oven to 450°F.
Cut the rutabagas into 1⁄2-inch-thick sticks. Pat the sticks dry with paper towels and place them in a bowl. Add the olive oil, rosemary, salt, oregano, garlic powder, and pepper. Gently toss to coat the rutabaga with the oil and seasonings. Arrange in a single layer on a large baking sheet.
Roast for 20 to 25 minutes, until golden and crisp. Sprinkle with the parsley and thyme.
Meanwhile, in a small skillet, combine the butter and the minced garlic. Cook over medium heat, stirring, for 1 minute. Whisk in the ketchup and hot sauce; cook until just heated through.
Transfer to a small bowl and serve alongside the fries for dipping.