Chop the tip and tail off of the turnips, peel them, and spiralize them using a spiralizer.
Add the kale, oil and pesto to a large skillet and heat to medium. Cook until kale has wilted, about 3 to 5 minutes. Add the turnip noodles and artichoke hearts and stir well until the noodles are coated in sauce. Cover and cook 8 to 12 minutes, stirring occasionally, until noodles have reached desired done-ness. Note: if noodles begin to stick to the bottom of the pan, add more oil or a couple tablespoons of water.
Serve pasta with pine nuts and freshly grated parmesan cheese if desired. (To keep this recipe vegan or paleo, skip the cheese).