Peel the rutabagas and cut them into roughly 2" chunks; place them in a large mixing bowl.
Add the rest of the ingredients to a separate bowl and mix vigorously with a whisk until well combined.
Pour that sauce over the rutabagas and toss with a spoon until all the pieces are evenly coated.
Spread the rutabaga in a single layer across a broiler pan, making sure there is plenty of room between the pieces of rutabaga to allow air to circulate freely.
Cover with aluminum foil and bake in the oven for 30 minutes, then remove the foil, lower the heat to 375°F and continue baking, stirring 2 or 3 times during the process, until the rutabaga is fork tender and starts to caramelize around the edges, about 25 minutes.
Once the rutabaga has reached the desired color and doneness, remove it from the oven and immediately hit it with a light sprinkle of salt. Let it cool for a few minutes and then serve, garnished with fresh herbs and a dribble of extra-virgin olive oil, if desired.