In a small bowl, whisk all ingredients for the dipping sauce together until combined. Cover and refrigerate until ready to use. Note: the sauce will thicken as it sits in the refrigerator.
Preheat the oven to 400 degrees F.
Whisk together the oil, dried thyme, garlic powder, ground cumin and salt in a small bowl.
Peel all of the root vegetables and use a mandoline slicer to slice them 1/8-inch thick. (You can also slice them thinly using a sharp knife, but be very careful, as roots tend to be difficult to cut.)
Use a brush to lightly coat both sides of each chip with oil, then place the slices on an oven-safe wire rack, making sure the slices do not overlap. Place the wire racks on 2 baking sheets. (If you don’t have enough wire racks or baking sheets, you can make the chips in 2 batches.)
Place the baking sheets in the oven and bake the roots until golden-brown and crispy. Check on the roots every few minutes once they have been baking for 20 minutes; remove any chips that are brown and crisp and return the rest to the oven until they’re all done baking.
Serve fresh out of the oven with buttermilk-parsley dipping sauce. Store any leftovers in a sealed bag or container - note that chips will not stay crispy after they have sat for a while.