Preheat oven to 400°. Peel parsnips and potatoes, saving peels. On a rimmed baking sheet, toss peels with oil, sage, and 1/4 tsp. each salt and pepper, and spread out evenly. Bake for 10 minutes, stir, then cook until golden and crisp, stirring another time, 4 to 6 minutes. Keep warm.
Cut parsnips and potatoes into 2-in. chunks, put in a medium pot with broth, cover, and bring to a boil over high heat. Reduce heat and simmer until parsnips are very tender when pierced, 25 to 30 minutes. Drain, reserving liquid.
Return vegetables to pot with 1 cup broth (save remaining broth for other uses) and beat with a mixer or mash until as smooth as you like. Add coconut spread, yeast, and remaining 3/4 tsp. salt and 1/2 tsp. pepper; stir well. Transfer to a warm bowl. Top with some of root vegetable strips and serve the rest on the side.
*Find butterlike coconut spread, such as Earth Balance, as well as nutritional yeast at health-food stores or Whole Foods Market.