To make the dip: Preheat the oven to 400°F Cut the garlic in half horizontally, keeping the head as intact as possible-do not peel the garlic. Drizzle the cut surfaces with the oil and season with a sprinkle of salt and pepper. Put the two halves back together to re-form the garlic head. Wrap tightly in aluminum foil. Bake until the garlic is tender and the cloves have turned golden beige, 35 to 45 minutes. Unwrap the garlic and let cool completely. Squeeze the garlic pulp out of the skins into a small bowl, discarding the skins.
Using a fork, mash the garlic pulp until smooth. Stir in the ricotta, Parmigiano, and sour cream. Season with salt and pepper to taste. Let stand* for 30 minutes at room temperature to blend the flavors. (The dip can be prepared 1 day ahead, covered, and refrigerated. Let it come to room temperature before serving.)
To make the chips: Using a mandoline or plastic V-slicer, cut the root vegetables as directed below. The slices should be almost paper-thin, less than 116 inch. As the vegetables are sliced, place each kind in a separate large bowl of cold water and let stand* for 30 minutes to remove excess starch.
Carrots and parsnips: Peel and cut lengthwise into very thin strips.
Beets: Rub your hands lightly with vegetable oil to keep the beet juices from staining your skin. Peel the beets and cut crosswise into very thin rounds.
Lotus roots: These can be found at Asian grocers, and make very interesting chips with random holes throughout. Peel and cut crosswise into very thin rounds.
Taro: Also known as yautia, this root vegetable can be purchased at Latino and Asian markets. Fried taro chips have a slight purple tinge. Peel and cut crosswise into very thin rounds.
Drain the vegetables well. Spread them out between layers of paper towels and pat completely dry.
Place a large wire cake rack over a jelly roll pan. Fill a large roasting pan with a double thickness of crumpled paper towels. In a deep Dutch oven, melt vegetable shortening over high heat to a depth of 2 to 3 inches and heat it to 350°F
In separate batches, without crowding, deep-fry the vegetables, stirring often with a wire-mesh skimmer to separate the chips, until the chips are golden brown, 2 to 3 minutes. (If you are frying beets, fry them last, as their color may leach into the oil.) Using the skimmer, transfer the chips to the wire racks to drain briefly, then move them to the roasting pan with paper towels to remove excess oil. Separate each new layer of chips with more paper towels. The chips will crisp as they cool, and are best served at room temperature within 6 hours of frying. Just before serving, sprinkle with salt and pepper, and serve with the ricotta dip.